There isn't really a significance. There are 20 "ancestral" amino-acids, while the genetic code uses triplets from 4 distinct nucleo-bases (ACGT) which yields 64 codons. Redundancy is unavoidable.

Now, why did the genetic code evolve based on triplets... that's kind of a million dollar question

However, there are significant or interesting properties and consequences of redundancy. Maybe this was the question you had in mind?