1
general::
Make an obscene gesture by closing one's fist and extending one's middle finger upward, generally interpreted as FUCK YOU. For example, Herb has a dangerous habit of giving the finger to motorists who cut in front of him. Although from about 1890 to 1920 this term was used in the sense of "disappoint or snub someone," that meaning seems to have died out. [Second half of 1900s]
American Heritage Idioms
2
general::
Phrase(s): give someone the finger
1. Fig. to display the middle finger upright as a sign of derision. (The gesture is derisive and offensive. See also flip someone off, flip someone the bird.) • Did one of you guys give Ted the finger? • Somebody gave the cop the finger. 2. Fig. Inf. to mistreat someone; to insult someone. • You’ve been giving me the finger ever since I started working here. What’s wrong? • I’m tired of everybody giving me the finger around here just because I’m new.
McGrawhill's American Idioms And Phrasal Verbs