A frame of reference is an arbitrary set of axes to which something happens in relation to -- or in particular, in physics for instance, a point (described by a set of coordinates) to which the position or motion of something (say, an observed quantity) is descrbied. We can see a frame of reference as a point to which we compare something, or relate something.
For example, if you have a car moving northwards at a speed of 50kph, and you are standing still at the side of the road, then you see the car travelling northwards. On the other hand, if you are also travelling (in another car) 50kph (side-by-side with the other car), then you don't see the car moving (at appears at rest relative to your position). Hence, we can say that a reference frame is related to the observer (though some physicists may still have a distinction between observer and frame of reference).
Another very simply example is orientation. If two people are standing on opposite side of the road (facing the road) and a car moves from left to right (from our perspective), the car moves from left to right to one observer, but right to left to the other observer. This happens because they have a different orientation, and hence a different reference point. (This is assuming that we are looking at what's happening from our screen, or from a bird's eye view; of course, we also have a different reference frame).
A reference frame can mean a lot of things in physics, but the essence is basically the same. The notion of a reference frame is also critical to the theory of special relativity (particularly the intertial frame of reference).