我关心你   <Wǒ guānxīn nǐ>        I CARE A…

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

关 is a part of the word 关系 <guānxi> a RELATIONSHIP
心 is a HEART

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