what does it mean to have two natures in one person?
Considering it has only happened only ever once in human history, your question is understandable.
I know He is both God and human,
That's correct, however Christ wasn't "half man half God", rather He was fully
Human and fully
God. To be fully human, He must have a complete
Human Nature and to be fully God, He must have a complete Divine
Nature. Now, these Two Natures, Divine and Human must be distinct, otherwise, if they become confused and melded , we end up with a third type of Nature which is neither soley Human nor Divine, but a combination of the two in One Nature (Monophysitism), and thwerefore, Christ would neither share the same Human Nature as us, nor the same Divine Nature as the Father and the Holy Spirit; but rather, would have a Nature unique to Himself. So the Two Natures are distinct, yet Christ is One Person, not two. Christ was the same Person before and after His incarnation, not "two different Persons". Before the Incarnation, Christ had only the Divine Nature which can never change. At the Incarnation, the One Person of Christ accepted and took on a Human Nature also. Thus He remains One Person Who is both fully Divine and fully Human. A complete Human Nature requires a Human Will, and a complete Divine Nature requires a Divine Will. Christ's Human Will was conformed to His Divine Will, but they were still Two Wills.