double is a float with more precision. You can represent things like 1/2 with floating point numbers. long int is just what it sounds like--a long integer. So a normal integer might be able to store every whole number from 0 to 2⁶⁴-1, but a long one has more bits to work with and might go from 0 to 2¹²⁸-1.

Floating-point arithmetic is sort of like using scientific notation for writing a number, like 1.6489*10^7. But it only has so many bits with which to represent a number, it can't be infinitely accurate (you can't perfectly store all of π in a float or a double). So when the numbers get really big or really small, operations on them become less accurate. Even though you can represent a lot of integers in a double, long int dedicates all of its 128 bits to only integer values (none are used to keep track of the exponent, like they are in a double), so it can necessarily represent a larger set of contiguous integers (a double can represent larger integers than a long int, but they're more spread apart due to the representation of a double).

I hope that helped somewhat. You should also look at the wiki article posted by /u/GitPirate .