Anatomically, the thumb is a finger. Colloquially, "finger" usually refers to one of of the other four appendages of the hand that is not the thumb.
Fingers are defined as digits that extend from the palm of the hand, which is why the thumb is considered a finger. Each finger has three bones except for the thumb which only has two; the thumb is missing the middle bone. Humans have an opposable thumb. In other words, the thumb moves in opposition to the fingers, so that it can swing around and help in grasping objects; it is critical for fine-motor skills.