Vim is a powerful, portable, keyboard based text editor. Being text-based, vim is lightning fast, with an incredible set of features developed over its multi decade existence.
Pro Vim understands code, and has movements and text objects reflecting this
Working on markup? The t text object allows you to move around based on tags. Simple text more your thing? w is the word object. Writing C-style code, chances are vim will recognize it, and allows you to jump to the next function, for example, using ]].
Pro Productivity enhancing modal paradigm
As with all vi-like editors, Vim provides a modal paradigm for text editing and processing that provides a rich syntax and semantic model for composing succinct, powerful commands. While this requires some initial investment in learning how it works in order to take full advantage of its capabilities, it rewards the user well in the long run. This modal interface paradigm also lends itself surprisingly well to many other types of applications that can be controlled by vi-like keybindings, such as browsers, image viewers, media players, network clients (for email and other communication media), and window managers. Even shells (including zsh, tcsh, mksh, and bash, among others) come with vi-like keybinding features that can greatly enhance user comfort and efficiency when the user is familiar with the vi modal editing paradigm.
Pro Has multiple distinct editing modes
Interaction with Vim is centered around several "modes", where purpose and keybindings differ in each.
Insert mode is for entering text. This mode most resembles traditional text entry in most editors.
Normal mode (the default) is entered by hitting ESC and converts all keybindings to center around movement within the file, search, pane selection, etc.
Command mode is entered by hitting ":" in Normal mode and allows you to execute Vim commands and scripts similar in fashion to a shell.
Visual mode is for selecting lines, blocks, and characters of code.
Those are the major modes, and several more exist depending on what one defines as a "mode" in Vim.
Pro Can never outgrow it
The fact that very few, if any, people claim to be a "Vim Master" is a testament to the breadth and depth of Vim. There is always something new to learn - a new, perhaps more efficient, way to use it. This prevents Vim from ever feeling stale. It's always fresh.
Pro Extremely portable
Vi/vim exists on almost all Unix-like platforms. It's the de-facto Unix editor and is easily installed on Windows. All you need to make it work is a text-based connection, so it works well for remote machines with slow connections, or when you're too lazy to set up a VNC/Remote Desktop connection.
Pro Keyboard-based, mouse-free interface, and trackpad support
There's no need to reach for the mouse or the Ctrl/Alt buttons again. Everything is a mere key press or two away with almost 200 functions specifically for text editing. Vim does support the mouse, but it's designed so you don't have to use it for greater efficiency.
Versions of Vim, like gVim or MacVim, still allow you to use the mouse and familiar platform shortcuts. That can help ease the learning curve and you'll probably find you won't want to (or need to) use the mouse after a while.
Pro Lightweight and fast
When compared to modern graphical editors like Atom and Brackets (which have underlying HTML5 engines, browsers, Node, etc.), Vim uses a sliver of the system's memory and it loads instantly, all the while delivering the same features. Vim is also faster than Emacs.