Purpose of dilution streaking or streak purification
The purpose of this technique is to dilute the bacterial cells so much that you get single cells, as can be seen on the image of the plate. You can then pick the colonies grown from these single cells, characterize them, test them for the mutations/plasmids, or whatever change you introduced, and can be sure that you have only the descendants of a single cell in your culture.

This way you ensure that you don't grow a mixture of different cells with different characteristics, of which one will eventually overgrow the other one. The streaking is a fast and reliable technique, which works especially well when you want to test a larger number of bacterial cultures. It also allows to check a stock culture very fast for contaminations with other bacteria by simply inspecting the single colonies by eye (different bacteria often look different).

Diluting the cultures would work as well, but needs to be done in more than one step and is more work when you want to do it for more than one culture. Also for dilutions you often plate more than one plate to be sure to have a plate with single colonies (when the cell number is unknown).