It does not happen each and every time l stop but sometimes when l apply the break, it goes smooth until it gets close to the floor then there is like the grunting (not grinding) noise and it almost seems as though the break is giving out.

Actually when it gets in that mode, the car seems to even move a little bit further beyond when l originally hit the break.

l do not know how else to explain it because I am very car illiterate.

This is a 1996 Lexus ES300.

You have a bad ABS (antilock brake system) sensor on one of your wheels. By the way it is BRAKE not break.

Do not mess around. Take the car to get serviced.

l recommend taking your car to a mechanic ASAP. It could be a problem with your Master Cylinder. A mechanic will be able to help you. Do not wait too long to get it checked out because it might cause an accident or get very expensive to fix.