1999 Pontiac Sunfire BRAKE and ABS light on

When I first got my car about a year or two ago, it was during the winter. When coming to a stop, the brake pedal would vibrate and my car would skid. About halfway through the winter, I believe my brakes kicked in? And the skidding stopped and my brakes worked much more properly. At that same time, the brakes dash light and the abs dash light flicked on, but since then (it's now June) they have still been on. Should these lights be on and should my brakes still be like this even though it's not winter anymore? Or should my brakes work like they originally did without the lights on my dash on?