Phones are simply compact computers. As such they can run any software installed on them. However, many people are unaware that they can get this software from anywhere. Google, Apple, and (to a lesser extent) Samsung have gone to great lengths to make it difficult or scare users away from installing software from outside their own platforms.
This site will introdce you to several alternative distribution channels for applications on the android platform with a particular focus on Free and Open Source Software (FOSS). There are several reasons that developers may not want to list or distribute their software through the Google play store. For instance, Google charges ongoing registration fees for developers to list their applications. Additionally, Google charges payment processing fees for paid applications. Perhaps most interesting is Google's history of delisting software that offers alternative front ends to their services or otherwise competes with their product offerings. Users additionally may feel uncomfortable with how much information that Google knows about them and may want to limit the use of Google services. In this case, using the Google play store is almost impossible since an account associated with their device with many telemetry services being enabled is required to download applications from the Play Store.
An app store framework and repository with a focus on extensibility, freedom, and open source software.
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You own your device. You should be able to do whatever you want with it! No company should control a monopoly on what software is approved to run on your hardware. This may seem hypothetical or soley a matter of principle to many users who haven't had issues with the play store but developers of many apps are expressing their displeasure with the status quo more and more. Closed ecosystems are not only bad for your rights to ownership but the ability of developers to share their inovations.