Pretty much nothing, but that's an interesting story in itself.
Let's assume that you're between the ages of 10 and 100 years old (luckily, many things in cosmology depend only on orders of magnitude). When the universe was the same age as you, it consisted of a soup of protons, electrons, helium nuclei, and radiation. But the soup was very hot -- the temperature was a few hundred thousand degrees Celsius. At that temperature, the radiation was actually more dense than the matter!
But in terms of exciting events, nothing much was going on. The two major events that we understand pretty well in the early universe are the formation of some of the light elements when the universe was a few minutes old, and the release of the cosmic microwave background radiation when the universe was a few hundred thousand years old. In all of the time in between, the universe just expanded and cooled. Or at least we think it did.
That long epoch between the first few minutes of the universe and a few hundred thousand years later is a kind of cosmic "dark ages." We don't think anything important happened back then, but we also have no way of probing this era. The universe was opaque to radiation, so we can't observe it directly, but we also have no indirect probes as we do for element production in the early universe.
So what was happening back when the universe was as old as you are now? Probably just experiencing middle-age spread. But we'll never know for sure.