Under rally point scoring, a point is awarded after every single rally, to whichever team did not commit the fault or get the ball grounded on its own side. It makes no difference which team served the ball that started the rally: the winner of the exchange scores, full stop. The team that wins the rally serves next, and if that team was already serving, the same player continues serving; if the receiving team won the rally, the serve rotates to them, and their players rotate one position clockwise before the next serve.
This is the system used at every top level of the sport today — the Olympics, the FIVB World Championship and Nations League, professional leagues, and NCAA and high school competition all score matches this way. It replaced the older side-out system, under which a team could only add to its score while serving; winning a rally on the other team's serve merely earned the right to serve next, without adding a point.
Reading a rally-scored set
Because every rally counts, the score climbs continuously and both teams' totals are visible running tallies of who has controlled play — there is no hidden 'side-out' bookkeeping to track separately. A set is won by the first team to reach 25 points (or 15 in a deciding final set, and 21 in beach volleyball) with a lead of at least two points; if the score ties at 24-24 (or 14-14, or 20-20 in beach), play continues past the target number until one team leads by two.
Why the change mattered so much
It is hard to overstate how much rally scoring changed the sport's texture. A team that was clearly weaker but happened to be serving well could no longer simply run out the clock on a side-out era set by holding serve; every rally, won by either team, directly moved the score. This raised the stakes of every single point equally, made comebacks from a large deficit both more mathematically tractable and more dramatic to watch since every point closed the gap by exactly one, and gave broadcasters a scoring rhythm close enough to sports like tennis or table tennis that international audiences unfamiliar with the older system could follow a match immediately.
