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But Lily was already up to her ankles in mud, little pools of water forming around her feet.

Everyone was up to his ankles in mud.

I read a sentence of "up to one's ankles in mud" and I found those exmples.

What does "up" exactly mean here?

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It means "as far as". The mud was deep enough that their feet sunk into it until their ankles were (at least in part) covered in mud. The surface level had risen, due to their sinking as far as their ankles. It's slightly confusing as the level of the mud does not actually rise it is the owner of the ankles that sinks.

The phrase "up to" is used in several similar contexts such as "up to your elbows in dish washing".

It can also mean having a lot of or too much of something, as in "up to your neck in paperwork". Whilst you do not literally have paperwork at neck level the image conveyed is of drowning in too much of it.

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