Just /re/ would find the next line in the file that matched
/re/command would find a matching line and execute the command
g/re/command would execute the command globally
that is, on each matching line
If the command was p, it would print the matching line:
g/re/p # print all lines maching a pattern
And that's where we get the word "grep"
GREP(1) GREP(1) NAME grep – print lines matching a pattern