This means that old people should be served first, and the beautiful and young
should be served or assisted later. However, it is mostly used by old people in
a funny way to flatter the young people. It's often rude for a young man to say
this to an older woman.
It is recorded that Mrs. Parker and a snooty debutante were both going in to
supper at a party: the debutante made elaborate way, saying sweetly "Age before
beauty, Mrs. Parker." "And pearls before swine," said Mrs. Parker, sweeping in.
[Disclaimer: I copied all the above elsewhere.]
Old age seems a stigma and handicap people don't want to face. It's humor for the
old to say "Age before beauty" but insolence for the young.