Each PvP League runs for a fixed amount of time. When one ends, another begins right after it. Each season has its own Leaderboard and rewards. The more trophies you have the higher chance of you ranking high enough for a reward tier.
Winning means you stand to win Epic Weapon Mods, Gold, and Eagle currency. The Leaderboards reset each time the PVP season ends. The season timing is displayed in the Leaderboard section.