Civic humanism is a term (first coined in the 20th century) used to refer to the ideas of republicanism. It is the idea that people should all participate in governing themselves. This is not just a personal right to freedom, it is also a responsibility that people have to their community. It also holds that this is how people truly fulfill their humanity. In other words, it says that people need to be part of governing themselves and helping improve their community if they are to fully realize their potential as human beings.
The connection between civic humanism and Florence is that the term was coined to describe attitudes in Florence in the Renaissance. During this time, some Florentines were coming to embrace this attitude as a solution to the dangers that their city faced. There were constant worries about being invaded by enemies. There were also worries about falling under the power of a tyrant. The idea of civic humanism arose in part as a way to justify the idea of having a republic and as a way to motivate people to stand up for Florence and republianism against those dangers.