Web3 or Web3.0 refers to an internet powered by various decentralized technologies; usually, cryptocurrencies of some sort (i.e., those with smart contracts) and the like, alongside distributed means of storing data like the Interplanetary File System (or IPFS).

Fireship.io provides a pretty good explanation of Web3 and how it works, though be aware that it's geared towards web developers and programmers more than the layperson: https://www.youtube.com/watch?v=wHTcrmhskto. You can probably find other videos on YouTube (or your preferred alternative) that describe Web3.0 in a more generalized sense.

The term comes as an increment of Web2, which is nominally what the internet is now. Web2 or Web2.0 is the general connecting of everyone; I am simplifying greatly, but it's the establishment of an actually social web of people who are connected to each other through the internet. Data flows in considerably massive quantities between entities, all connected to each other to achieve great things.

Web2.0 itself comes from Web1 or Web1.0, which is the early internet. Think static pages on static web servers. It is the bare-bones internet, where you simply ask for something and get it back; you ask for a picture and you get that picture back, you ask for a news article and you get that news article back. The concept of a user's identity on the internet or a website isn't well established, if at all; and therefore the usage of such an identity to customize a page for a specific user doesn't exist.