On a ground ball, that would be the second baseman as he/she is running towards the throw from third, as opposed to the shortstop who would be running away from the throw, and would be in a better position to make a quick pivot and throw to first to complete a double play than would the shortstop.
CLARIFICATION: "Who covers what base" depends on these factors:
-- where the ball is hit
-- how it is hit (line drive, ground ball, pop fly)
-- how many outs are there
-- are there baserunners and where are they
-- what is the positioning strategy of the infield (playing normal depth, playing in, playing shallow)
-- even what pitch the pitcher is signaled to throw by the catcher!
If you were able to see all the players on any hit balls you would see almost a ballet of movement, as they each run to their respective positions-- rarely going to the same spot twice, as all these factors vary each time.
This is just one element of the tremendous amount of learning that goes into the training of a baseball player.