Wanting to
pot the pink but being 'snookered' behind a red and having to attempt a
difficult brown.
This is in relation to the cue
sport's rules where the pink ball is worth more points than a brown, however the touching of the red ball is a foul move.
The context of the joke is wanting to have normal sex, however your girlfriend or wife is on her period. Instead you are forced to convince her into having anal sex.
The term is mainly used in countries where snooker is a popular sport.