Degenerate Alignment Analysis
First, degeneracy in a basic sense refers to redundancy of the codons in the genetic code.  For example, the amino acid proline is coded for by one of four codons: CCA, CCC, CCG and CCU. The third codon position (the third letter in each group of three) is called four-fold degenerate because it can change without affecting the coding for proline. Phenylalanine is two-fold degenerate because it is coded for by UUC and UUU.

However, this does not account for the alignment part of your question. Without more specific information (such as a reference you saw), I can't be certain of your intent but this paper by Morin et al. (2008) may be helpful. They had a series of small RNA sequences (each about 24 nucleotides long). They wanted to identify DNA sequences in the genome of Lodgepole pine  (Pinus contorta) and rice (Oryiza sativa). To accomplish this goal, they used degeneracy alignment. Here's the relevant section from their methods:


  altered to allow searches against genomic sequence. Alignments were kept if they were no shorter than L − 3, where L is the query sequence length. No more than a total of three mismatches or insertions/deletions were allowed within the aligned region.


Their approach was to find genomic sequences that correspond to the small RNAs. They allowed for some degeneracy, either in the genome or the RNA. The sequences could differ in length by no than three nucleotides or mismatches (an A in the query sequence but a C in the target sequence instead of a T; I'm assuming the query is RNA and the target is the genomic DNA). Their degeneracy alignment allowed for a small amount of freedom in identifying potential matches of conserved RNA clusters (high similarity) in the genomes of distantly related plant species. 


  Morin, R.D. et al. 2008. Comparative analysis of the small RNA transcriptomes of Pinus contorta and Oryza sativa. Genome Research 18: 571-584.