The Apache License 2.0 is a permissive open source license and can be used in any kind of software, including paid applications. This is very similar to the MIT license. However, the Apache license is much more detailed and legally precise.
- Like the MIT license, you must give any recipients of the software a copy of the license and copyright notices. The Tink project does not contain any very visible copyright notices, but some files contain a “Copyright 2017 Google” statement.
- If the project contains a NOTICE file, you must include a copy of that file as well. Tink does not contain a NOTICE file.
- If you modify Tink, you must add a “prominent notice” to modified files. You can however license your modifications under whatever terms you wish, as long as you otherwise comply with the license.
The Apache license has one big advantage over the MIT license: it includes an explicit patent grant, at no cost! Google cannot sue your for patent infringement for your use of Tink. This patent license terminates if you claim in a lawsuit that some part of Tink is patent infringement, but that doesn't matter if you don't hold any patents. The MIT license does not provide similar legal certainty with regard to patents.
As to how you should display the Apache license and the copyright notices in your application, you would usually show an “Open Source” menu item in your app's settings screen. See also my answer What to keep in mind when releasing an app which uses libraries licensed under the Apache 2.0 License? on Software Engineering.