cherish is more intimate. You can cherish the friendship of a good companion while you might appreciate the support of a colleague at the office.

Hello Alina! To "appreciate something/someone" means to recognize how good someone or something is and to value him, her, or it .... I think that another way of saying it is "to be grateful for something/someone". For example; "I really appreciate my new car as I see my friends driving old cars and some of them don't even have a car and I am reminded of how fortunate I am." To "nurture something/someone" means to care for and protect (someone or something) (especially while they are growing). So an example would be the way parents lovingly take care of their children - emotionally, spiritually and physically, so that they are always well taken care of and happy. or The way that people take care of the plants in their homes or gardens. I hope that helps!

I agree with the other comments, cherish is more intimate and also implies that you value someone the way that you would value your most valuable possessions or a priceless treasure. Here is a popular song that uses this word. https://www.youtube.com/watch?v=nJztW9dcpyc