By pruning a plant’s shoot tips, its lateral buds will grow out, producing branches. This will briefly reduce the amount of leaf area since resources must be reallocated to the side branches, but the amount of branching and the leaf area index (driven by the new leaves of the multiple lateral branches) will then be greatly increased.
Work Step by Step
The thing to see here is that a removed shoot tip releases lateral buds to grow out, each producing many leaves. You can skip ahead to the chapter on hormones/signals for more details on this process.