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In an LTI or a LTV system, the input function can be represented by a continuum of time-shifted impulse functions, combined "linearly".The system's linearity property allows the system's response to be represented by the corresponding continuum of impulse responses, combined in the same way.
The time-invariance (TI) property allows that combination to be represented by the convolution integral. Its used mainly for amplifying or attenuating the multiplicative factor (or the values having the most influence) independent of other values.
For time-variant sytems, the combination is represented by the superposition integral. Google it for more info.
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