Mike Cohn says in his book Agile Estimating and Planning that he originally used 1, 2, 3, 5, 8, 13, 21 as his sequence until a client said to him "You must be very confident to estimate the size as exactly 21 and not 20 or 25". He realised that 21 was too precise, so he changed it to the vaguer value 20.
8 is bigger than 5 and smaller than 13. It's much bigger than 3 and much smaller than 20. Some teams use other sequences such as doubling: 1, 2, 4, 8, 16, however, in my mind that makes it too precise. It seems to be claiming that a 16 is almost exactly twice as big as an 8. I prefer the vagueness of the modified Fibonacci sequence. If a task is twice as big as an 8, it's probably a 20 because we tend to underestimate rather than overestimate. It also allows for "about 50% bigger", so 50% bigger than 8 is 13, again slightly inflated.
I find that the Fibonacci sequence has the right balance between precision and vagueness. However, the Fibonacci sequence is just one sequence for estimating the size of each task. Obviously each team should use the values that work for it. If you find that some other sequence works better for your team, by all means, use it.
