The four angles of a chart are the points where the circles that define it cross the ecliptic: the ascendant on the eastern horizon, the descendant opposite it in the west, the midheaven at the culmination, and its opposite below the earth. Greek astrology calls them the kentra, the pivots, and the houses that begin at them are the angular houses, the first, fourth, seventh and tenth.
What the tradition claims for them is strength. A planet in an angle acts with more force and more visibility than the same planet anywhere else, and the strength is understood as a matter of position rather than of dignity. An ill placed planet on an angle does its ill work loudly, and a well placed one in a cadent house may do its good work where nobody notices. The distinction between a planet's essential condition, meaning what it rules and where it is exalted, and its accidental condition, meaning where it falls among the houses, is one of the load bearing distinctions in traditional judgement, and the angular group is the clearest case of the second.
The four are not equal to one another. The tenth and the first are generally counted the strongest, with the seventh and the fourth below them, and authorities order the lower two differently. The ranking matters in practice because a chart usually has several candidates for its strongest planet, and this is what breaks the tie.