Dictionary:

smart aleck

  (ăl'ĭk)

1. A person regarded as obnoxiously self-assertive.
2. An impudent person.

[Perhaps after Aleck Hoag, 19th-century American confidence man and thief.]

noun

One who is obnoxiously self-assertive and arrogant: malapert, witling. Informal know-it-all, saucebox, smarty, smarty-pants, wisenheimer. Slang wiseacre, wisecracker, wise guy. See good/bad.

An impudent or obnoxiously self-assertive individual, a wise guy, as in New teachers often have a hard time coping with the smart alecks in their classes. This expression, dating from the mid-1800s, probably alluded to a person of this description who was named Alec or Alexander, but his identity has been lost.

The noun has one meaning:

Meaning #1: an upstart who makes conceited, sardonic, insolent comments
  Synonyms: wise guy, wiseacre, wisenheimer, weisenheimer