How does the Fibonacci sequence relate to Pascal's triangle?
The Fibonacci sequence is related to Pascal's triangle in that the sum of the diagonals of Pascal's triangle are equal to the corresponding Fibonacci sequence term.
This relationship is brought up in this DONG video. Skip to 5:34 if you just want to see the relationship.
Just adding onto Bartholomew's answer.
As mentioned, the values on the 'shallow' diagonals of Pascal's triangle add up to the Fibonacci numbers.
In mathematical terms:
This can be visualised below: