An edge piece of a puzzle is normally a piece that has two stickers (because it is part of two faces). On the 3x3x3 there are 12 edges, and for each pair of adjacent colors there is only one edge with those two colors. On larger cubes (such as the 5x5x5), however, there are several edge pieces for each pair of colors, as you can see in the image of all edge pieces on the 5x5x5.
On larger cubes there are actually two types of edge pieces: midges and wings. A midge (short for 'middle edge') lies exactly in the middle of the edge, and can be flipped in place. A wing, however, is not symmetrical, and actually has only one orientation if you know where on the cube it is located. This means that if there are two (say) red-white wings on a cube, they cannot be interchanged without being flipped, and you cannot flip just one of them no matter what the rest of the cube looks like.