There are a couple situations for moves that are obtained "at level 1" (Bulbapedia lists them as learned at "Start"):
For a Pokemon's first evolution, either by being caught (at levels low enough to not have learned many moves from level up) or hatched, their move list will be populated by these level-1 moves. Hatched pokemon may have a number of these moves replaced by those passed down by their parents, like egg moves.
For the other uses, often on more evolved Pokemon, I like to point to Aegislash. It learns no moves by leveling, yet it's signature move that allows it to transform back to to the defensive shield forme, King's Shield, is a 'level 1' move, and not learned by it's prior evolutions. In cases like this, the intended way to obtain these moves on the Pokemon is through the Move Reminder.