Let’s say you desperately need a cup of tea. So you buy a cheap 4-way extension cable and 4 electric kettles. You fill all the kettles and turn them on at the same time for maximum tea-making throughput.
The combined load of all the kettles exceeds the rating of the extension cable.
With a fuse: the fuse in the extension cable plug blows, you buy another fuse, and learn some patience.
Without a fuse: the extension cable overheats and causes a fire, your house burns down, and worst of all you still don’t have any tea.
In the UK, there's typically one ring circuit and one lighting circuit per storey, a separate ring circuit for the kitchen, and dedicated circuits for large current draws such as an electric oven or hob, shower, or immersion heater.
Each circuit would have a dedicated MCB (Miniature Circuit Breaker) which will trip if too much current is drawn. The standard MCB rating for a ring circuit in the UK is 32A.
The combined load of all the kettles exceeds the rating of the extension cable.
With a fuse: the fuse in the extension cable plug blows, you buy another fuse, and learn some patience.
Without a fuse: the extension cable overheats and causes a fire, your house burns down, and worst of all you still don’t have any tea.