Milestone leveling replaces experience points with story progress. Instead of tracking XP, the Dungeon Master levels the whole party up when they reach a meaningful beat — clearing a dungeon, defeating a villain, or finishing a chapter of the adventure.
The big advantages are even leveling (nobody falls behind for missing a session) and zero bookkeeping — no adding up monster XP after every fight. It also lets the DM pace the story directly, leveling the party right when the narrative calls for it rather than when a spreadsheet says so.
The trade-off is losing the "earn every point" feeling some players enjoy, and the party can’t grind extra fights to level faster. Many published adventures mark milestone points for you; otherwise, a good rule of thumb is to advance a level every 2–4 sessions in the early tiers.