There are a few common ways to understand Dante's use of the word "shade," which is translated from the Italian "ombra." This can mean, literally, a shadow or the shade cast by an object, but for Dante, a shade is the spirit of a dead person, so in a sense it can be thought of as a kind of ghost or essence. Another meaning for "ombra" can be "trace." All these meanings enter into Dante's use of the word.
Dante's most famous shade, of course, is the shade of Virgil, who guides Dante through hell. In the first canto, when Dante first comes upon Virgil, Dante is not sure if Virgil is man or shade, but Virgil explains that he is "not man; man once I was," meaning that Dante has come across Virgil's spirit or ghost.
Dante meets many shades of famous people on his journey. Some of these are characters from the Bible and classic literature; for instance, in canto 5 he sees among the tormented lovers Helen, Cleopatra, and Tristan, among others. Some are figures from Italian politics or even Dante's personal acquaintances. In canto 29, Dante encounters the shade of his real-life classmate, Capocchio. Dante uses the idea of the "shade" or spiritual essence to show these characters for who they "really" are or to reveal their true character.