In IFR flight you sometimes need to accurately time seconds for approaches or turns.
Early watches did not have a "seconds" hand. Some watches had a small secondary dial for seconds, but because of the small size it was hard to read. The rule was written "sweep-second hand" meaning a seconds hand that swept around the main dial so that a pilot could accurately time seconds.
As "fooot" says above, it does not refer to the type of motion the hand makes.
I have seen some aircraft equipped with digital clocks and often wondered if I needed to wear a "sweep-second hand" watch to be legal.