Aberration is a classification of monster introduced to the Dungeons & Dragons lexicon during third edition. Designed to help assist in collating the vast array of monsters into more useful groups, the Aberration classification ultimately came to be the dustbin of monster categories. All the freakish and weird and extra-gribbly monsters ultimately ended up being classified as aberrations, a tradition that continues to this day. The book Lords of Madness was a book dedicated to aberrations which went into great detail about the lore of them.
Pro-tip: if it looks like it could kind of come out of the works of H.P. Lovecraft, or is a direct rip-off of those critters, it's probably an aberration. Psionic powers are also a pretty common theme, too.
Some of the most iconic D&D aberrations are: