The second unit, in the making of a movie, is a camera crew
charged with filming all manner of things that don't involve the
stars, or dialog, or other such trivialities. The second unit films
scenery, long shots, closeups, and shots involving stuntmen
and doubles.
While the first unit is filming Harrison Ford flying the 747, the
second unit is filming[1] a hand pushing the throttle (but not Ford's
hand).
After Jamie Lee Curtis seductively lets fall her gown, or
Robert de Niro roars off after robbing the bank, the second
unit gets the shot of the dress lying in a heap on the floor, or the
license plate of the car.
It was the first camera that showed us Robert Redford
in the cockpit of a biplane; the second actually went up in a plane and
captured the soul of the African savannah.
While the director is in control of the making of the movie as a whole,
the second unit has its own director. Working from the storyboards
and pre-production planning with the director, the second unit director may
(particularly if the director has worked with him before and knows and trusts
his work well)
go off and get all the shots that will be needed, and deliver them to the
director (eventually, the editor) who will interweave them with the primary
shots.
[1] The second unit may be right there with the first unit getting all the
filler shots while the location is still set up for filming, or they may be somewhere
entirely different getting shots that don't involve the principal cast.