A non-terminal is any Action which provides at least +1 Action. These cards allow you to play more Actions after them and so chain cards together; any number of non-terminals can be played on a single turn. This differentiates them from terminal actions, of which only one may be played each turn without assistance from villages.
Cards that provide +1 Card and +1 Action have the nickname "cantrips"; these can usually be played with no penalty to yourself either in handsize reduction or lack of extra Actions. Any non-terminal Action that provides more than +1 Card is non-terminal draw, and any card providing more than +1 Action can be referred to as a village.
Special Treasure cards that have Action-like abilities are sometimes classified with non-terminal Actions, as are Night cards, because, like non-terminal Actions, any number of Treasures or Night cards can be played on a turn without affecting your ability to play terminal Actions. Thus, for example, Loan or Monastery might be described as a "non-terminal trasher", in the same category as an Action card like Lookout.