Browser history
Browser history is the dated list a browser keeps of the pages you opened, searchable by page title and address, and held for weeks or months depending on the browser. If you are signed in to a browser account with sync switched on, that list is not confined to the device you made it on.
Where you see it
In the browser's history menu or panel, and less obviously in the address bar - a few typed letters can complete into a site you visited, which is where most accidental exposure on a shared device happens.
Why it matters
Sync is the part people miss: deleting history on a phone may leave the same entries on a laptop signed in to the same account, and the deletion has to reach the account, not just the device. Clearing history also stops at your browser. It does not touch the platform's own login and viewing records, a search history held in your search-engine account, or a card statement.