If the pot is an odd number, say 49, and is to be split between two players. How to do that? 24.5 each? or round up to 24 and 25? In the latter case, it's not fair.
Typically the "odd" chip is awarded to one of the players based on the type of game: in positional games (like Holdem or draw, with blinds) it is given to the player in earliest position; that is, the first player counting clockwise from after the dealer button. In stud-type games, it is awarded to the player with the highest card in hand (or lowest, in Razz), ties broken by suit if necessary.
In high-low split games, odd chip goes to high. In some hi/lo games like Omaha, there's an additional rule that players being quartered get the odd chip. I.e., if one player wins high and two players split low, then the low half gets the first odd chip (and when that is split, if there's still an odd chip, it's awarded by position).
The odd chip must be of the lowest denomination in play, or change must be made first.
In home games, of course, you can make your own rules: odd chip goes to the beer fund, or stays for the next pot, etc.