If the float in your bilge is up and the pump is not operating then you need to correct that immediately. You probably have a disconnect in the wiring between the float switch and the pump itself, probably because of corrosion. Check all the contacts, connections, and splices if you have any between your float and your pump, then check all the connections back to the battery. If those all are fine, then replace your pump. Corrosion ate through the connections on my float and my pump stopped working. I almost lost my floor, but luckily my high water alarm went off and I was around to hear it (this was after what I can only assume is weeks of the bilge slowly filling). When I went to inspect the connections on the float, the wires disintegrated to dust in my hands. No joke, they became powder, rubber and all, the corrosion was that bad. I fixed it by removing and replacing the corroded elements and everything worked fine again.
As to where the water could be coming from there are two possibilities. Unfortunately, if your seriously concerned about the water, your going to have to taste it to figure out which (just dip your finger and taste a drop or so). If the water is sweet then the water is coming from the rain, and it is fresh water. This is normal, as boats usually take in some water when it rains. If you get excessive water, then check various seals and deck fittings for leaks. Fresh water is generally not a problem though, so as long as your bilge can pump it out then whatever. If the water tastes salty then it is obviously from the sea and that could mean that your keel bolts are leaking. That would be the least desirable because that would mean a huge job of taking the keel off to re-bed it immediately. Other salt water possibilities could be from your stuffing box, if your engine bay drains into the bilge, and/or your rudder packing. Both of those can be fixed with a crescent wrench and a screw driver.
Your always going to have some water in your bilge, I always have a quarter of an inch or so, because I can't find a pump that can remove the water when it gets shallower then that. So don't fret about a small amount of water. However, if your bilge is always full, even when your pump is working, then check some of the things I listed above and fix it. Its annoying to hear water sloshing around in the bilge when sailing.