How can output sequence be equal to the sum of copies of the impulse response, scaled and time-shifted signals?

I am sorry, this is a very basic question. But i am having hard time understanding is how it is possible.

I know impulse response is the output of the system when impulse sequence is given as input with initial conditions set to 0.

Scaling is to increase the amplitude of the signal, i.e. if i multiply the input by 2, output will also be multiplied by 2.

Time shifted signal is if I delay the input then the output is also delayed by the same factor.

Now can some one please illustrate this with an example how any sequence can be decomposed into sum of copies of the impulse response, scaled and time-shifted signals?

Thanks a lot in advance.