What does "I am all yours" mean?

In the sentence

If you can change his idea, I am all yours.

What does I am all yours mean?

It's used in various settings, with different meanings.
Your example is a fairly uncommon case; it means "If you can get him to agree, I will support you wholeheartedly." We don't usually use the phrase in such a serious manner.

More commonly, it's used when people are making social/entertainment plans; in that case, it means "I'm ready / I'm not busy (or don't have other plans) at the moment / your suggestion sounds good to me":
"Are you ready to go?" "I'm all yours."
"Bob, do you have a minute to go over the sales numbers?" "I'm all yours."
"Want to meet for drinks after work?" "I'm all yours."

If you're not familiar with the idiom, this phrase can sound a lot more meaningful than it's usually meant to be - be careful not to read too much into it!

I'm all yours means, I'm at your disposal (= I am ready to help you in any way I can).