You really have to sit down and see a vim user work to start to understand.

In vim you don't just move around with arrows, then delete and then replace the text you want. What happens is you can use noun-verb associations to do things.

For example on a line like this:

    var foo = "bar";

I could be at the beginning of the line and type the following keys to change the inside of the quotation marks:

    ci"baz<esc>

In sublime I would do the following:

    <cmd>→←←⌫⌫⌫baz

The difference between the two was an epiphany for me. In vim I could actually use verbs and nouns to determine how I will edit the text in front of me. I now have a language that I can use to edit text rather than editing the text using the most manual of tools and the verbs and nouns combination are only limited by my imagination and the plugins I install.