A sequence of numbers is an infinite list of numbers. The individual numbers in a sequence are called terms. If you can wrap your head around a sequence, that may be referred to as "coming to terms with infinity."
The terms are separated by commas, and "..." is written at the end to show that the sequence continues forever. Or that the sequence is lost in thought and trailing off.
Sample: 1, 2, 3, 4, 5... is a sequence. The 1st term is 1, the second term is 2, and so on.
Non-Sample: 2, 3, 4 is not a sequence, because it does not go on forever. No little dots means this baby is three and done.
Sample: 0, 0, 0... is a sequence where every term is 0. And what a scintillating sequence it is.
Because a sequence is a pattern, you can find any term of the sequence as long as you're given enough terms to figure out where it's going. With even natural numbers, for example, you can determine that the 350th term of the sequence would be 700 (2 x 350). Beats writing out the first 350 terms by hand. Unless you're in prison, and are looking for activities to pass the time.
Here are some more fun sequences.