The Lesser Gods are the step below The Worldly Gods. They are not necessarily their children, though this can be the case. I would likely classify a lot of the supernatural beings in many real world Religions which tend to refer to Spirits as being Lesser Gods (note: this is not actually a comment on anything related to real world religions, the term lesser hear doesn't mean that any real world religion is “lesser” than any other). That being said, I definitely wouldn't classify them all that way, many religions which talk about spirit have origin stories which also involve spirits, those spirits would most likely be at minimum Young Gods, but more likely Old Gods or Universals.
The Lesser Gods, despite being called lesser, are still extremely powerful. Many of them could probably wipe an entire country off the map, but they just aren't as powerful as The . They also will probably have far more interactions with mortals, maybe even live among them. They will probably make for both good antagonists, and companions/helpers in various historical events and/or stories.
Not all worlds necessarily have Lesser Gods. It will really depend on both what feels right for a given world, as well as whether or not the given Worldly Gods, Young Gods or Old Gods for that world would even have had any interest in making something like them.