Degenerate PCR is in most respect identical to ordinary PCR, but with one major difference. Instead of using specific PCR primers with a given sequence, you use mixed PCR primers. For instance if you just have a protein motif, you can back-translate the protein motif to the corresponding nucleotide motif. Example of a degenerate PCR primer designed after a protein motif. The more wobbles you introduce in the PCR primer the more degenerate it gets.
Most genes comes in families which share structural similarities.
By aligning the protein sequences from a number of related proteins you can find which parts of the protein is conserved or which is variable. Based on this information you can find conserved protein motifs which can be used as a starting point to make degenerate PCR primers. You have isolated a protein and have managed to sequence some amino acids from it. You have found a human gene and want to clone the homologue gene from i.e. Mouse or Drosophila. Phylogenetic and evolutionary studies of genes.