What is the difference between Clicks and Visits?

Visit in Google Analytics can be understood as the start of a session. i.e, the 1st pageview of every session is a Visit (which is equal to number of sessions, this is the reason visits are replaced by Sessions in Google analytics). Visit is a Session level metric.

Click is the click of the mouse on the website, which is an interaction metric. So, a button can be clicked, link can be clicked, video can be clicked etc.

Clicks indicate the number of times a user clicks on your ad. Visits indicate the number of unique sessions associated with each of the visitors. Google Adwords tracks click. Google Analytics tracks visit.

Clicks: It indicates the number of times user clicks on your ad.
Visits: It indicates the number of unique sessions associated with each of the visitor.