Let's say I need to change a word. With Gedit, I double-click the word and retype it the right way. With Vim, I press j until I'm on the line where the word is, then I press w until I'm at the beginning of the word, then I press cw to change the word, retype it the right way, and press escape to go back to command mode.
Triple-clicking in Gedit highlights a line. Triple-clicking and dragging highlights a contiguous group of lines. In Vim, I'd need to move to the line I want to begin my selection on ([number]G or jjj), then press V, then press jjj until everything is selected. And I don't have to deal with the fact that the default way of deleting things overwrites the default clipboard either.
I do use Vim when I need to process lines in a text document (with macros), when I'm editing files on a server, or when I'm writing a git commit message. I suppose I could use Vim in much the same way as Gedit through its mouse capability, but I dislike the lack of interface between my system clipboard and Vim's, and the fact that when I paste code in to a Vim document, the indentation gets all screwed up.