It shows that said Sgt is a member of the RAuxAF, as in A for Auxiliary. Dress regs were changed a while back removing the need to wear the A on all forms of uniform (technically, you had to have an A on 'normal' rank slides, as well as collar dogs on No1s and No5s). It's all part of the 'whole force concept' don'tchaknow...
I know plenty of us 'Oggies' who are quite proud of our heritage and status and who routinely 'forget' to take them off.