The TYPICAL law of motion of capital
$k_t$ is your capital after investment, so if you subtract the capital you carried over from last period, $k_{t-1}(1-\delta)$, you obtain the amount that must have been invested in order to have $k_t$ of capital today. 

Remember that $k$ is a stock variable, while $i$ is a flow variable. This is why the flow $i_t$ is the difference between the current and the former stock: $k_t-k_{t-1}(1-\delta)$.