1.5°C is the average across the entire globe, but because of the way global warming influences the climate, this will result in much more extreme temperature variations on a local level.

For a somewhat hyperbolic example, imagine that wherever you live ranges between 60-80°F on an average year, the average temperature then would be ~70°F. If the temperature range were to change to 22-120°F due to climate change, then the average temperature would only be one degree higher but temperatures on any given day could be unbearably hot or cold.