To address the reason this probably appeared ungrammatical, note that it would be a mistake to write:
that you have read and you have understand
These wordings, which are similar in meaning to the wording you have proposed--"that you have read and understood"--are grammatical:
that you have read and you have understood
that you have read and you understood
But as RageFoxx points out, that's not quite the desired meaning.
This wording has the desired meaning and is grammatical:
that you have read and you understand
The existing wording--"that you have read and understand"--has that as its intended reading. It is likewise grammatical, because it can be read that way. (Strictly speaking, it must be read that way, since the other possible reading--"have understand"--doesn't make sense.)