Chop is a term in poker that has many different meanings. The meaning being used depends on the context:
Split A Pot
The most common usage is "to split a pot and award it to more than one (tied) winner". This is common in games like Hold 'em where the existence of community cards leads to a greater frequency of equal hands.
Chop is not used as a term when a pot is split between high and low in a hi-lo split game like Seven-card stud hi-lo. In games like those, players merely talk about "winning high" and "winning low", or "scooping" (winning both). If, however, the high or the low half of the pot is itself divided among more than one player, it could be called "chopping" that portion of the pot, though it is more often referred to as "quartering", for the obvious reason that we're down to a quarter of the total pot now.
Tip A Partial Chip
In games where chips are of a denomination higher than $1 (for instance, a $20/$40 game played with $5 chips), players who wish to tip the dealer an amount that is less than one chip will toss the dealer a chip of any particular denomination and ask the dealer to "chop it". The dealer will break the chip into smaller denominations, including one or more $1 chips, will keep one $1 chip, and return the rest to the player as "change" for the tip.
Asking the dealer to chop a tipped chip is implied to mean you want to tip the dealer $1, a standard tip amount. If you wish to tip them more, you simply toss them back some of the change they hand you (or tell them up front "keep $2 of it"). In low-limit games at Foxwoods, players may hand the dealer a $2 chip and say, "Me and you," to indicate that they expect $1 in change.
Cancel a Hand by Having Both Blinds Withdraw
In California, due to the fixed-fee rake structure imposed by state law, it is often advantageous for the small blind to simply sacrifice the rake (if any) from their blind if all other players have folded to them, and withdraw the remainder. This has come to be known as a "chop", and is considered courteous (and may even be financially to the small blind's advantage -- see the rake page for more details). Since it is essentially robbing the big blind of the remainder of the small blind (remember that the small blind could always simply fold and donate their blind amount to the big blind), it requires approval of both blinds. But the big blind, unless they have a big hand, often realizes that having the small blind call and then playing out the hand could result in a net loss to both blinds, with only the house rake coming out ahead. This is usually only true given the (relatively large) fixed-fee rake structure found in California, but even outside of California, the blind players may sometimes chop a hand in order to save time and be courteous. Chopping etiquette holds that consistency is the most important virtue, so that even a powerful hand should be chopped if one has chopped previously with the same opponent or has agreed to do so.
Interestingly, some casinos may prohibit chopping in this way (for example, the Mandalay Bay has a house rule that prevents chopping). I'm not sure why, but it's always best to ask the dealer as well as the other blind if you'd like to chop.
- Chop-chop? (2+2, April 2006) - discussion of merits and etiquette of canceling the hand