Boiling starts when vapour bubbles can form throughout the liquid.
A liquid boils when its vapour pressure reaches the pressure outside it. That is why boiling temperature changes with altitude.
Small bubbles can appear before boiling because dissolved gases are leaving the water.
At normal atmospheric pressure, pure water boils at about 100 °C. A pressure cooker raises the pressure and lets water get hotter.
At higher altitude, atmospheric pressure is lower. Water can therefore boil at a lower temperature than at sea level, which can affect cooking.
A useful way to understand this phenomenon is to separate the driving force from the visible result. Temperature, pressure, concentration, surface area and the nature of the materials can each change the rate or the final state. In real systems, several of these factors often act at the same time.
That is why the same phenomenon can look different in a laboratory, in the kitchen or outdoors. The underlying chemistry or physics stays the same, but the conditions change the balance.