With the LNAV/VNAV approaches it is possible to fly GPS approaches to a decision altitude just like an ILS. If you fly a LNAV only approach you level off at MDA and continue on to the missed approach point.
Flying the LNAV/VNAV approach requires some pretty fancy equipment and many of the older FMS equipped aircraft are not certified for it, even though they have VNAV capability.
What the FMS does with barometric VNAV is the same thing you can do in your head when flying a visual approach. With a GPS it is relatively easy to go direct to a runway. If you are visual you know that a 3 degree glideslope is 300' per nautical mile. So if you are 5nm away from the threshold, you should be at 1500' AGL. If you are one mile away, then you should be at 300'.
The FMS uses the aircraft's air data computer (a bunch of sensors and electronics that are used to generate the altitude and airspeed data displayed to the pilots and by the FMS to solve time, fuel, distance problems) and the the position data generated by the GPS sensors to create a pseudo glide slope. This makes it possible to fly an ILS like approach with no ground based navaids. The only problem is that you require an accurate altimeter setting and there can be some rather large errors caused by extreme temperatures. This is why you will almost always see a note on the plate that LNAV/VNAV minimums are not authorized below -15 degrees C. You can check out table 7-2-3 in the AIM to see why.
It is also true that LNAV/VNAV does not always give you lower minimums. There are many approaches where LNAV and LNAV/VNAV minimums are the same or very close to each other. Other times you can go several hundred feet lower using the LNAV/VNAV minimums. It just depends on where the obstacles are on the approach. If you pay attention, you will notice that even if the LNAV/VNAV approach allows you to descend to a lower altitude, they often require a higher visibility than the LNAV only approach. This is due to the fact that the LNAV/VNAV approach is flown to a DECISION ALTITUDE, not a MDA, so you must be able to see the runway from the missed approach point. If your LNAV/VNAV approach allows a DH of 300', you will require about 1 mile of vis. to see the runway from this point. On a LNAV only approach, you may get by with a lower visibility, but risk an unstabilized approach with higher descent rates to make the runway if you see it after passing your visual descent point.
If you are not flying LNAV/VNAV approaches, it is best to just cross out the minimums. It is not uncommon for students to bust the IFR checkride by trying to descend to the lower LNAV/VNAV minimums when they are flying a GPS approach.
If you do fly an aircraft capable of these approaches, the FMS may also contain visual approaches as well. All you do is pick the runway and the length you want your final to be and the FMS will create an ILS like approach that you can fly by following the flight director. Other older FMS units may be capable of the same thing, you just have to do more work to construct the approach. The key to these is that they are for visual use only and should not be used as a substitude for an instrument approach. They do not assure terrain clearance. If you are in mountainous terrain the point you create for a 5 mile final could easily be inside the mountain.
Eventually WAAS will allow us to do all this more accurately and with cheaper equipment, but for now LNAV/VNAV is about as good as it gets without an ILS.