Definition
algorithmic problem solving technique that split into many simple subproblems and reduce steps of subproblems. In other wards, separates into subproblems and get solution by addition of all subproblems.
Example
if you calculate $2^1+2^2+2^3+2^4+2^5$ and display each numbers,
$2^1=2=2$
$2^2=22=2^12$
$2^3=222=2^2*2$
$2^4=2222=2^32$
$2^5=22222=2^4*2$
since you need to calculate each of numbers ($2^1,2^2,2^3,2^4,2^5$), you can skip some of parts that you already calculated. When you calculate the $2^5$, you done have to calculate $2^4$ if that number $2^4$ is already calculated.