Apparently for the same things as with XML/JSON/TOML.

> I followed the link and read the page, but I’m still not sure what the point is!

According to the website:

> It has no data types, no semantics, no underlying model of cons cells or anything similar. It’s as close to pure generic syntax as it gets.

> So at the lowest level Jevko is a minimal formal specification for flexible trees of text.

For its simplicity it seems quite powerful to me. I don't see it replacing JSON/markdown or even TOML. But is seems trivial to implement on very low-level, older, less bloated, or less powerful systems.