Although it isn't a perfect science, IP addresses can be turned into physical addresses with increasing accuracy. There are public databases that show which ISP owns which IP address with a good sense of which region they use it in. There are private databases with more accurate information. And, of course, the ISP knows the exact service address of each IP address.
VPN services can mask a device's IP address from a web server. When a VPN service is engaged, all traffic is encrypted and routed through the VPN server. The web server only sees the IP address of the VPN server. This is sufficient for maintaining anonymity from web server operators and advertisers, but it isn't sufficient for maintaining anonymity from oppressive regimes which might be able to lean on VPN operators to turn over their logs showing the original IP addresses. Those looking for safety from such regimes or desiring to blow the whistle on government agencies need something more.
The Tor (The Onion Router) network was designed for just such purposes. It bounces encrypted web traffic through at least three independent servers that volunteer bandwidth to the project. None of the servers have enough information to identify both the IP address of the original computer and the final destination. Therefore, any government agency wanting to access the information would have to compromise all the machines in the link, which are dispersed over the globe. This doesn't provide perfect privacy, but it gets pretty close.
The Tor project has an app for Android called Orbot, which is available on F-Droid and everywhere else Privacy Browser is distributed. Orbot can operate in three modes.
Currently, Privacy Browser works with Orbot in transparent proxy and VPN modes. Support for the standard proxy mode will be added in a future release.
Because traffic is being routed through several Tor nodes, using Tor is often much slower than going straight to the internet.