What does 'kokoro ni' mean in Japanese?

Literally "to heart", as in taking something to heart.

"Kokoro" means heart (usually pertaining to ones feelings). "Ni" is a particle that is added to confirm time, direction, or purpose (it can mean to, at, in, on, per, from, and by). You might say "watashi no kokoro ni sore o kanjiru", for I feel it in my heart, or "kokoro ni sore o toru koto wa arimasen" - don't take it to heart.