Some boats have a hydraulic ram at the base of the baby stay so it's adjustable. If it does it's meant to be used for tuning - mast bend, draft position, etc. If it's not adjustable then it's just there to prevent pumping.
In a conventional sloop rig there is an upper shroud that goes from the deck to the masthead. There are two lowers on each side, one forward of the mast position and one aft of the mast position. Some boats have a rig with a single lower and a babystay instead of forward lowers. This babystay replaces the forward lowers and is essential to the stability of the rig. On these rigs the existing lower is either aft of the mast or even with the mast. This allows more bending of the mast for efficiency on various points of sail. Either way it is essential and shouldn't be removed.