To understand Wobble Hypothesis, one needs to recall the "degenerate nature" of the genetic code that states "an amino acid can be coded by more than one codon". Such codons are called synonymous codons. In most of such synonymous codons, the first two bases remain same while the difference arise in the third base only.

For example, codons GGU, GGC, GGA and GGG all code for same amino acid, i.e., Glycine. 

Thus, the position of third base on such codons is called "Wobble position".

Now, it is already known that a t-RNA has an anti-codon sequence complementary to the codon sequence on the mRNA that translates for an amino acid.

Frequently, it has been observed that one tRNA can translate more than one of these synonymous codons, sparing the cell from making multiple tRNAs to carry the same amino acid. This phenomenon is known is known as Wobble.

Therefore, according to Wobble hypothesis proposed by Crick (1966), the third base on a codon has least influence on the meaning of synonymous codons and thus its pairing with the anti-codon sequence on the tRNA could vary from the usual Watson-Crick base pairing. Thus, the Wobble hypothesis explains the possible cause for the degeneracy of the genetic code.