A square is an angle of 90°, a quarter of the 360° zodiac. That makes it the aspect of the 4th harmonic: divide the circle by four and every point you land on is square or opposite the starting point. Harmonic astrologers read the number four as the number of structure, effort and manifestation, which is why squares and oppositions share a family resemblance. Four squares form a cross, and three planets linked by two squares and an opposition form a T-Square.
By whole sign, a square joins signs three apart. Those signs always share a modality: Aries, Cancer, Libra and Capricorn are all cardinal; Taurus, Leo, Scorpio and Aquarius are all fixed; Gemini, Virgo, Sagittarius and Pisces are all mutable. But the elements do not combine easily (Fire meets Water or Earth, Air meets Earth or Water) and the polarities differ, one yang and one yin. Same rhythm, different temperament: both planets want to act in the same way, but toward different ends.
The exception is the out-of-sign square, where the degrees are about 90° apart but the signs are not three apart. Mars at 29° Gemini and Saturn at 2° Libra are 93° apart, a square by degree, yet Gemini and Libra are both Air signs, a trine by sign. Most modern astrologers still count it as a square, often noting that it feels a little softer or less obvious than an in-sign one.
Worked example. The wheel at the top of this page shows the Sun at 4° Aries and the Moon at 7° Cancer. Here is how to check the aspect: