The organelle that has its own DNA and provides energy to both plant and animal cells is the mitochondrion.

Here's why:

* Its own DNA: Mitochondria have their own circular DNA molecule, separate from the cell's nuclear DNA. This suggests an ancient symbiotic relationship where a bacterium was engulfed by a eukaryotic cell and became a permanent resident.

* Energy production: Mitochondria are responsible for cellular respiration, the process of breaking down glucose and converting it into ATP, the cell's main energy currency.

While chloroplasts in plant cells also have their own DNA and are involved in energy production (through photosynthesis), they are unique to plant cells and don't provide energy to animal cells.