What part of the idea are you having trouble with? I'll try to do my best with the general idea, but if you need something more specific let me know.

State functions are characterized by the idea that no matter what path you take to get from point A to point B, the difference between B and A remains the same. An example of how this works can be illustrated using gravitational potential energy. Say you lift a box 5 meters vertically straight up into the air from the surface of the ground (which we shall set to a height of 0 m). You increase its energy by an amount mg :delta: h where :delta: h = 5m. Now say that you lift a box from the ground level up 1 meter above the ground, walk to the right 5 meters, lift the box 1 more meter, walk to the left 2 meters, raise the box 7 meters, walk to the left 1 more meter, and lower the box 4 meters. How much did the gravitational potential energy change? The same amount as before, mg :delta: h where :delta: h = 5m, because the box is still only 5 meters above where it started in either case and the potential energy depends only on the final height minus the initial height (it depends only on the final and initial position).

In contrast, you expended a lot more energy (more work) moving the box around than you did just standing in place and lifting it straight up. So the work you did is NOT a state function. This function depends on the path. When you lifted the box straight up you did less work than your body did lugging the box around left and right while lifting it up and down. So the potential energy is a state function, but the work you did is a path function.

Now in thermodynamics you usually apply these ideas to the 1st law or conservation of energy:

U = Q + W

In this example, Q and W are path functions...the exact amount of work you do or the heat transferred to the system depend on how you add the heat or do the work (these individual values will vary depending on whether or not you did these things in either a direct or roundabout way). However, if you add these two path functions together the overall result, U, is a state function. It only depends on Ub-Ua, regardless of whether or not you did direct or roundabout Q's and W's.