The latch is the mechanism that keeps the door shut without a key and opens when you press the handle or turn the knob. In Spanish, picaporte is the word used in many areas for the latch bolt itself and, by extension, for the door handle or the door knocker.
On internal doors in a home, the latch is the only fastening there is: it holds the door so that a draught does not blow it open. On front doors it is combined with a key-operated bolt.
If the latch stays pushed in and the door will not catch, it is usually a worn return spring or a strike plate that is no longer in line with it. Both can be fixed without changing the door. You will find this under lock installation and lock repair.