Ending an utterance with a verb in its て-form makes a short, casual request. It is natural with family and friends, or when an urgent situation makes the intended request obvious.
How it works
The listener is normally understood to be the person who should perform the action, so the sentence can end immediately after the verb. Relationship, context, and intonation tell the listener that the form is a request rather than merely an unfinished sentence.
Typical casual requests
These requests are short because the relationship or situation makes the intended action clear.