What a politician does (or should be doing if s/he
hopes to get elected) during the run-up
to an election. It means to make contact with the voters by means of personal skin to skin contact (but hopefully non-sexual), such as shaking hands and kissing babies
. In a general sense it implies getting out
and getting in the face
of as many different voters as possible because if they meet someone they're probably more likely to have a positive opinion
of them than the candidates that they didn't meet in person.
Mr. Bush probably doesn't need to go out and press the flesh because he is running for re-election based on his first term record.