What does "Time To First Byte" (TTFB) mean and what can I do to improve it?

I keep hearing about Time To First Byte (TTFB), what does it mean? Does improving it make my website faster?

Webpagetest define this as

The First Byte time (often abbreviated as TTFB) is measured as the time from the start of the initial navigation until the first byte of the base page is received by the browser (after following redirects).

Most of the TTFB is usually related to the time it takes a webserver to produce the HTML. While this is taking place, the user will generally be viewing a blank screen so improving the TTFB goes a long way toward improving user experience.

Serving HTML from cache is a super way to improve TTFB. Otherwise, code and network optimisation is the go,