If the government spends, say, $100, then somebody's income goes up by $100. That is, the initial, first round increase in income is $100. This is in turn, spent on something else or saved -- depending on the MPC. The additional spending is, in-turn, saved or spent by the next person. And so on, creating the multiplier.
In the case of taxes, if someone gets a tax cut of $100, that person, we assume, will increase spending and savings according the MPC. So, the initial, first round, increase in income is 100*MPC.