Why do cells divide (or copy themselves)?
The "Why" question

Why do organisms replicate?

Given that there is (extrinsic and also eventually intrinsic) sources of mortality, organisms that did not replicate just ended up disappearing. Those that did replicate eventually ended up giving rise to important lineages.

In other words, replication occurs because those who did not replicate disappeared. It is also because unique instance of things may disappear that you regularly backup your computer (if you do).

The "How" question

By what mechanism did early replication occur?

You actually did not really ask about it but here are a few words anyway.

The mechanism by which first replication occurred are mainly unknown as it is hard to investigate specific processes that occurred such a long time ago. The field that studies the origin of life is called abiogenesis. You might especially want to read the section on Self-enclosement, reproduction, duplication and the RNA world. You might also want to read about Autocatalysis.

I am afraid that a summary of existing hypothesis on early reproductive systems are 1) out of my capacity and 2) would hardly fit into the wish to receive a very (VERY VERY) easy explanation.