Something that's handwritten is written with a pen or a pencil — not typed or printed. A handwritten thank-you letter is a pleasant surprise these days.
Formal documents are almost always typed or sent electronically, and not handwritten. It's increasingly common for letters, invitations, and birthday greetings to be sent this way as well — which makes handwritten notes and greetings all the more intimate and meaningful. If you send handwritten invitations to a party, you write each one out by hand.