spin spin couplingWatch
The two methyl groups contain 6 equivalent protons. Each one of these protons can have a spin state of plus or minus 1/2, and each of these conditions creates a different local magnetic field.
The adjacent CH proton experiences 6+1 = 7 different fields and has 7 corresponding signals in the NMR (multiplet = many peaks).
The signal due to the two methyl groups (equivalent protons) experiences two different local fields due to the two spin states of the CH proton. Hence the two methyl group protons (sall equivalent) are split into a doublet (two peaks).
This influence of protons on the protons attached to neighbouring carbon atoms is called spin-spin coupling.