Assuming you don't use any particular browser and stick to some of the popular ones (such as Google Chrome or Apple Safari) you tell to the Internet a lot of things, at least the following,
- IP: assigned to you by your ISP and so linked to the ISP's subscriber's service
- Browsing behavior: to the browser's vendor, possibly some details as well to the OS vendor
- Tracking details: to the website you are visiting (cookies), to invisible (and embedded) tracking software, to the advertisement software that allows for these in the website you may be visiting, to other third parties that may be providing some service for the website or your browsing (Adobe Flash...)
- Browser fingerprinting: you would be surprised how unique it is to you (could be in the previous category of tracking, but it is worth its own category)
Moreover, there is the part of your personal information, anything you give can be used to track you. Although in some cases it is necessary, such as logging in some site to uniquely identify you.
As said by @J.A.K. it is about linking information, but there is the part of those who know you and provide details about you, something that you have little to zero control, and this can also be used to track you and eventually identify you as well (think of someone mentioning a nickname you use in some website that you registered).
@Alpha3031 pointed at a couple of interesting test sites of such browser fingerprinting and tracking within a site.
You may want to use TOR and browser the web via the TOR browser (https://www.torproject.org/projects/torbrowser.html.en). It will reduce your footprint at the expense of a slower browsing, and possibly degraded user experience if you are really committed to minimise any leak of information of your browsing habits.