An aspect is the geometric relationship between planets and/or points, based on them being a certain number of degrees apart.
When two planets are a certain number of degrees away from each other (give or take a certain "fudge factor" called an orb), these planetary energies interact with each other and combine their energies in a particular way, according to the aspect involved.
For example, some aspects are stressful but motivating (Square: 90°, Opposition: 18°0), some indicate talents or easy flowing energy (Trine: 120°, Sextile: 60°), and some are irritating but promote awareness (Quincunx: 150°, Semi-Sextile: 30°).
Aspects are sometimes indicated in a chart wheel by drawing lines connecting planets/points that have a particular aspect relationship.
Aspects most often refer to the measurement along the arc of the ecliptic (along the zodiac). However, parallels might also be regarded as aspects in that they compare the distance between two planets or points, but instead of being measured along the ecliptic, they compare the number of degrees each is north or south of the celestial equator.