With your densely packed DNA, you can afford to hold a lot more genes[1], to express a lot more proteins.
Additionally, you need to move around - your energy demands are so high that you can’t just wait around and hope. To this end, any change which makes you able to move, no matter how small, will be copied around the community. Eventually, those small changes add up to something called a flagellum.
However, this flagellum needs a lot of energy.
You can detect the presence of chemicals you can use, and move toward them using your flagellae. The sea around you is full of tiny little prokaryotes. They are made of chemicals…
You engulf smaller things, such as prokaryotes, which you want to take apart, and consume the energy, but on at least one occasion, something really odd happens.
Perhaps its outer wall is a little thicker, or perhaps you don’t quite have the right chemistry to eat through it, but anyway, you eat it… and it survives!
You’ve got another organism inside you. Ewwwww.
The prokaryote inside you lives on, and, protected by you from most other threats, eventually loses the genes it isn’t using. What is left, is a pretty simple thing, no longer an organism, but an organelle. It’s called a mitochondrium and it converts chemicals from one form to another for you.
With enough mitocondria inside you, you have plenty of energy. You might even have enough to drive two flagellae. You could really motor along!
[1]Instead of ‘stealing’ genes in the process of eating other chaps similar to yourself, when a pair of you meet up, one ‘gives up’ some genetic material to the other. If this sounds crazy, because the organism giving up material will lose out, you have to remember that genes are survival machines both in themselves, and in groups. In this case, the gene may well get the chance to make many more copies of itself when it joins with a new set of partners.
To facilitate all of these things, one major change takes place: the cell wall becomes less thick, and eventually forms a cell membrane.