Ok in very simple terms when a PSU has multiple rails it means that it splits up the power into two or more parts adding up to a more powerful PSU. They do this because back in the day they thought it would be unsafe to have to much power in a PSU so that's how they did it. On the label on the side of the PSU look and see if there's more than one 12v+ rating. Or try to find the model and make of the PSU.
If you try and run a GPU that takes more power than the PSU can handle it simply won't work, depending on what GPU your looking to buy will determine how much power you need in a PSU. Here is a good quality PSU that I have a feeling you'll end up needing before you can upgrade your GPU: http://www.newegg.com/Product/Product.aspx?Item=N82E16817151094
(if you look at the close up of the sticker you'll notice that this particular unit has 2 12v rails)