Here's a breakdown:

* Endosymbiosis: This refers to a relationship where one organism lives inside another.

* Theory: This means it's a well-supported explanation, but not definitively proven.

* Mitochondria: These are the powerhouses of our cells, responsible for generating energy (ATP) through cellular respiration.

The Endosymbiotic Theory states that mitochondria were once free-living, aerobic prokaryotes (bacteria) that were engulfed by larger, anaerobic prokaryotes (cells lacking the ability to use oxygen). Over time, a symbiotic relationship developed, with the engulfed prokaryotes evolving into the mitochondria we know today.

The theory is supported by several pieces of evidence:

* Mitochondria have their own DNA: This DNA is circular, similar to bacterial DNA, and distinct from the cell's nuclear DNA.

* Mitochondria replicate independently: They divide by a process similar to bacterial fission.

* Mitochondria have their own ribosomes: These are similar to bacterial ribosomes.

* Mitochondrial membranes: The double membrane structure of mitochondria is consistent with the engulfing process.

This theory is also supported by the fact that chloroplasts, found in plant cells, also have their own DNA and replicate independently. They are thought to have originated from a different type of prokaryote – photosynthetic bacteria.