More particularly, random number generators aren't really random at all - which is why they are more correctly called pseudorandom number generators. They are simply complicated formulas that take one number as input and produce another number as output. The special part is that the formulas are designed so that the output number appears to be random and uncorrelated with the input. But giving it the same input will result in the same output, every time.
When you want to generate a string of random numbers, usually what one does is simply take the output from the last time and use it as input the next time. But you have to have somewhere to start. That starting value, from which all the future random numbers will be generated, is called the seed.