The point is actually not to get as many points. That's just your personal score. It means as much to winning as your K/D/A (nothing).
The scoreboard at the top shows the HP of both team's Nexus. It starts at 500 and to win you must drop the enemies to 0.
Under the scoreboard at the top you'll notice some dots. There are 5 total and are red, gray or blue. These represent the 5 control points on the map. Gray means uncaptured and neutral. Red is enemy controlled. Blue is Friendly controlled.
Every couple of seconds, the team that controls less points loses 1 hp from their Nexus for every less control point they have. If one team has 3 points and the other has 2, the team with 2 points will lose 1 Nexus hp per second. Let's say the losing team makes one of the opponent points neutral. Then both teams would control 2 points each and one is neutral. Neither team would lose points.
Controlling points isn't the only way to drop the enemy Nexus HP though. Kills will also drop it by 2 as long as the nexus has more than 100 hp left.