There’s a strong chance that your browser offers a “private browsing” mode.
This was commonly discussed as a mode which you were supposed to use when buying a present for a loved one, so that they would not find traces of your secretive gift habits if they happened to use your computer. In reality, it’s pretty much universally known as “porn mode”, for much the same reason.
If you do not want your browser to retain a record of what sites you have visited, private browsing mode is reasonable way of doing this — it saves you having to clear your history, cookies, cache etc manually.
But private browsing does not stop the sites you visit from logging information about you, such as your IP address.
And it does not change any visibility which your network provider has of your traffic.
So it can be a useful tool, but be aware of its limits.