我关心你    /Wǒ guānxīn nǐ/        I CARE ABOUT YO…

我关心你
   /Wǒ guānxīn nǐ/
       I CARE ABOUT YOU, I AM CONCERNED ABOUT YOU

关 /guān/ is a part of the word 关系 /guānxi/ A RELATIONSHIP
心 /xīn/ is A HEART

TO CARE about someone is to have our mind (HEART) linked, connected, “relationshiped”, to the HEART of someone else.