“Appreciate” is often used wrongly.
Imagine that you are having a discussion with someone, and he says “I appreciate what you are saying”. Have you heard that sentence before? Probably. It is wrong. What the person probably means is that he “understands” (comprender) what someone has said.
To appreciate something is be thankful (estar agradecido) or grateful for what someone or an organization has done. “Appreciate” does not mean “understand”.
Here is a correct example: I appreciate the help you have given me.
This means that you have valued (apreciado) the help given to you, because that help was useful and you feel grateful. The noun is “appreciation” and you can correctly say “I showed my appreciation by giving him a box of chocolates”.