I like to compare it to being a first class citizen. Basically the right to freely move across boundaries in the country without being questioned of your purpose.
Note that in languages which support first-class functions, the name of the function does not play a big role. The name is just a variable pointing to the location of the function definition.
This might sound trivial to existing JS developers, but it is actually a boon. First-class functions are a necessity for “Functional Programming” paradigm.
Other languages which support them include PHP, Lua, Perl, Python, and Io.