A betting round is a clearly-defined stage in a poker hand where betting occurs. Different variants of poker have different numbers of betting rounds, and have them at different times in each hand. Each variant defines its own rules for when betting rounds occur during a hand.
Betting rounds always start with one active player at the table, who is still involved in the hand (i.e., has not folded) and has chips with which they could bet. Different variants have different rules for determining which active player goes first. That player must take an action in the round, after which play continues to the next player at the table who is still involved and has chips, moving around the table in a clockwise fashion. That next player must then take an action, at which point play continues to the next clockwise player, etc.
When the betting round has completed one full circle around the table, if no player has taken an aggressive action (that is, if no player has bet), then the betting round is over, and the poker hand continues according to the rules of the variant being played.
If one or more players have taken an aggressive action, then the betting round continues clockwise around the table until the most recent aggressive action has been closed. This is achieved either by all active players other than the most recent aggressor folding, or by all active players other than the most recent aggressor calling the aggressor's bet or raise.
Betting rounds may use any of the standard betting structures used in poker, which define the amount of money a player is allowed to bet or raise if they choose to do so. They may also have additional rules imposed on them by the house, such as having a cap on betting or a maximum pot size.