What it can look like at home
Oil burners lock out when the primary control does not see a safe, steady burn. That can happen for more than one reason: fuel delivery, ignition, a dirty nozzle, poor draft, air in the line, a blocked filter, delayed ignition, or another condition. The homeowner job is not to diagnose the burner. The useful job is to describe the pattern: when it locked out, whether fuel was recently delivered, whether the tank is low, whether the system was serviced recently. Also note whether Smoke, soot, or oil smell is present.
Why it can happen
A reset button is tied to burner safety control. When the control does not confirm proper flame, it shuts the burner down instead of letting it keep trying. Repeated resets can dump unburned oil into the chamber or make a delayed ignition problem more dangerous. That is why a reset is not the same thing as repair.