The genetic code is described as being degenerate. What does this mean? and why ?

We say that the genetic code is degenerate because there are several codons, which code for the same amino acid. For example UCA, UCU, UCG and UCC all code for Serine. 

This is due to the fact that mRNA coding for an amino acid only has 4 possible letters A, U, C and G and that there are 20 amino acids that need to be coded. If codons consisted of only one letter we would have 4¹ =4 possible combinations (not enough combinations to code 20 amino acids) if codons consisted of two letters 4² = 16 (not enough combinations to code 20 amino acids) only when codons consist of three letters we get  4³ = 64 combinations and we have enough combinations to code for 20 amino acids.  However 64 is a lot more than 20, therefore different 3 letter combinations (codons) are used to code for a single amino acid.