Estimation in agile can be performed using various tools, as long as it is based on relative sizing of stories (effort required to complete one story as compared to the other). Fibonacci series is just one of those tools. Some teams use the 't-shirt sizes' to estimate, Small, Medium, Large, XLarge. In short, planning poker (agile estimation) does not require the use of Fibonacci series for estimations.
However, Fibonacci series does help in providing arbitrary numbers which are not exact multiples and increase exponentially. So numbers like 4, 6, 10, etc. are out of the picture. Exponential increase is required to express bigness as well as uncertainty. A story which is, lets say, bigger than a 5-points story will remain big, so the team should not spend time in figuring out if it is a 10 or 11. Fibonacci series makes your life easier by not having a 10 or 11 and the team has to use either a 8 or 13 for the bigger story.
As the story size increases, it becomes difficult to precisely estimate (which requires that the story needs to be broken down first). Using precise numbers such as 34, 55 for uncertain estimates does not provide much value. So some teams follow a practice of using numbers having larger differences between each successive number. So they stop using Fibonacci series after 13 and use 20, 40, 100 or 20, 50, 100.
Actually there is no hard and fast rule about it other than ease of use, as agile recommends to use whatever works best for you.
This is what is mentioned on Mike Cohn's Mountain Goat Software site:
Why do the cards deviate slightly from the Fibonacci sequence?
We’re anal software people, too. We know that the Fibonacci sequence
should go from 8 to 13 to 21. We use 20, though, instead of 21. Of
course we used 21 in the early days, but dropped it after meeting with
a product owner who looked at the 21 and said, “Oh, a 21. You must be
very confident to give such a precise estimate. Most people would have
called it 20 or 25, but you called it 21.” We replied that we used the
Fibonacci sequence. The product owner said, “The Fibo-what?” After
which, we decided that deviating from the Fibonacci sequence would be
better because the numbers started to imply a very high level of
precision that just wasn’t there. The 1/2 is included because after
awhile some teams decide they want some room in between “free” (a
zero) and one. Using 1/2 isn’t something a team should do a lot, but
it’s a nice option to have in some cases.