A book that I love that covers this in an accessible manner is "Power, Sex, Suicide: Mitochrondria and the Meaning of Life" by Nick Lane

Basically, it looks like a single cell, predatory amoeba of some sort engulfed a parasitic bacterium that was the ancestor to mitochondria, and instead of being digested, it ended up living inside the amoeba, helping to produce energy.

This is a big deal because the way that cells harness energy is by doing some cool biochemistry across a membrane. When a cell has to rely on its main, cell membrane to do this, then the energy production is proportional to the cell's surface area, which means that it's proportional to the cell's radius squared (E ∝ r^2 ) . However, the energy requirements of the cell are determined by its volume, which means that energy requirements are proportional to cell radius cubed ( E ∝ r^3 ). For small numbers the difference between r^3 and r^2 isn't much, but as radius increases, the cell volume far outstrips its surface area, which means that there was an upper ceiling on how big a cell could get while still fulfilling its energy requirements.

Mitochrondria allow cells to break this size limit by decoupling energy production from cell size, because scaling up energy production is as simple as having more Mitochrondria. Mitochrondria have their own independent genome - in the years since the endosymbiotic event, the mitochrondrial genome has shrunk a lot, because it's sort of like moving in with a friend who already has a house full of furniture - no sense in having duplicates.