Say you want to know the value of some function at x=c. The limit x->c is the value of the function as x becomes very very close to c. Infinitely close in fact. You can find limits with your calculator entering x=c+.00001 etc and see what the value of the function is as you get very close to c.
Remember to approach c from the positive and negative sides, if you don't get the same answer the limit does not exist.
This "hole" you speak of is a good example. The function is undefined at one specific point. So you can't know exactly what the value of the function is there. But if you observe the value of the function as you get very close to that point you can see what the function would be so to speak.
Also, there doesn't always have to be a "hole". You can find a limit anywhere on a continuous function. For example.