In the map of the sky that is the astrology chart, the positions of the planets are noted by the sign they are in and, more precisely, the degree they inhabit within that sign, each sign being 30° wide. The twelve signs have a fixed position relative to each other: Taurus always follows Aries, Sagittarius is always three signs away from Pisces, and so on around the zodiac, forming the backdrop or the playground in which the planets play. Therefore, any planets in those signs at a given moment will reflect this relationship with each other. Specific relationships between planets are called planetary aspects, and the nature of the aspect is determined by the distance between two planets. A planet in the middle of Sagittarius will be in a square aspect to a planet in the middle of Pisces because these signs are always 90° apart (three signs apart at 30° width each). Therefore, by extension, the planets are also in a square: 90° apart.
However, because the planets move and their relative position to each other is not fixed like the signs (until we freeze them into place in an astrology chart for a time and place), they can wind up anywhere within the range of 30° of a sign when a chart is calculated. A planetary aspect is therefore defined more specifically by the actual degree distance between two planets, with a little bit of room for orb allowance. (Orb is a term that describes the allowable distance between two planets that are in aspect but are not exact.) So, the relationships between the signs and relationships between the position of the planets (as defined by the sign they are in) are not exactly the same, but there's often agreement between the two. A planet in Sagittarius will usually square a planet in Pisces, because those signs are square each other, unless those planets happen to be too many degrees apart where the distance is considered too wide to be an acceptable orb, in which case, the planets are not considered to be in aspect at all with each other.
For every rule, however, there are at least one or two exceptions!
An out-of-sign aspect happens when there are two planets in aspect to each other, but one planet is at tail-end of its sign, and the other is very near the beginning of its sign. When this occurs, the actual mathematical distance between the planets and the fixed relationship between the signs they are in tell a contradictory story. A planet in Sagittarius and a planet in Pisces should be square each other because the signs themselves are always square each other, but if a planet is at the end of Sagittarius (28° or so) and another planet is at the beginning of Pisces (2° or so), the actual distance between the planets as measured by degrees would put them about 60° apart from each other (64°, to be exact), which is a sextile, not a square. In this case, the precise distance takes precedence, and the aspect between these two planets would be defined as a sextile, with a 4° orb.
An out-of-sign aspect can be confusing to interpret because the signs in question may interact naturally in a different way than the actual degree aspect would dictate. If two planets are in a sextile as calculated mathematically by degree but in squaring signs, do they get along easily or not? The short answer is yes, both.
To interpret an out-of-sign aspect, contemplating each component and interaction separately first can provide some clarity. The order in which you do this doesn't matter as long as it makes sense to you. Consider the planets involved and the kinds of needs they represent on their own. Then, think on the mathematical aspect between them and whether makes it easy or difficult for them to come together. Next, consider the two signs involved and what style of interaction and need-fulfillment they represent individually. Then, think about whether their natural zodiacal relationship makes them interact easily or with some strife because of their respective styles and come up with examples of what the interaction might look like.
Let's walk through an example. To stay focused on the out-of-sign component, we'll isolate just two planets in two signs.
Aspect: Mercury in 29° Scorpio and Mars in 2° Pisces
By sign they're trine, but by degree they're square (93° apart).
First, contemplate Mercury and Mars on their own. Mercury represents the human need to learn, think, and communicate. Mars represents our will, from which stems our drive, passion, actions and pursuits, and how we handle conflict.
Mercury and Mars are in a square, so when there's conflict, disagreement, or "static" between these two, that means that how we learn, how we think, and/or how we express our ideas and opinions may somehow cause irritation to or friction with our passions, how we take action, or our conflict style. One possible scenario for this showing up in our lives might be a tendency to express ourselves in a way that we don't prefer or that gets us into trouble whenever we get angry or find ourselves in an argument.
Mercury is in Scorpio and Mars is in Pisces. Think about what Scorpio and Pisces have in common. They are both water signs, so the foundational basis for their style comes from an emotional and intuitive basis—what they feel in their heart and gut is a priority for them both and a baseline for their reactions to life. But since these planets are squaring each other, think about how the signs they are in, although usually in agreement in some ways due to their natural trine, might also (or instead) have their differences amplified because of the square energy between the planets.
With Mercury in Scorpio's desire to speak the truth and to acknowledge (and have others acknowledge) what they see and know that lies just underneath the obvious and Mars in Pisces's desire to act peacefully and kindly, they may often find that they struggle to work out how to do both. It may not be impossible, but there may be times when their sharp and to the point truth-telling desire is in conflict with their desire to not stir up trouble or to avoid painful conflict. Their ability to turn the other cheek may be ideal for them, but at times they may be unsure how to be do so without having to hide some of their true opinions. The resolution may lie in the trine that the signs naturally share: to keep it in the heart. Their lessons may be in finding the narrow path between honesty and kindness, to tell the truth without cruelty or to soften it (not bury it) with humor and compassion.
A whole-sign aspect is little more straightforward to understand and relies solely on the fixed relationships of the signs to one another, with no consideration of a planet's specific degree. A sign that is three signs away from another sign is in square to that sign, so a planet in each of those signs would be considered a whole-sign square, regardless of whether those planets were at the beginning, middle, or end of their respective signs. A planet anywhere in Sagittarius is in a whole-sign square to any planet anywhere in Pisces, even if the orb allowance would put them 20° apart or more!
While it may seem too imprecise, whole-sign aspects can be quite useful when considering the basic differences or similarities of each sign to each other and imagining them interacting. Even if not in aspect by degrees, a planet in Aries is going to act in a manner totally baffling and maybe frustrating or offensive to a planet in Cancer and vice versa. To have Venus in Cancer wanting to take care of and be taken care of by a kind partner but the Moon in Aries not wanting to be coddled could be quite confusing for a person because the basic nature of these needs conflict. No matter what the specific degree of these planets were in a natal chart, the tense nature of the square that naturally occurs between these signs given their position to each other in the zodiac would reveal itself in the personality. Whole-sign aspects can be especially useful in relationship astrology for this same reason; the differences or similarities between signs can enable conflict or harmony no matter what the math says.
Check out more tips on troubleshooting the chart in my book, Essential Astrology: Everything You Need to Know to Interpret Your Natal Chart.