Continuous integration (CI) is a development practice that requires the developers in a team to integrate their work regularly, often multiple times per day. Every push to the main repository is verified by an automated build. This practice helps with detecting problems as soon as possible, thereby speeding up development, and increasing the quality of the code. The great Martin Fowler wrote an article about the subject that explains the concepts and describes the best practices (http://martinfowler.com/articles/continuousIntegration.html)
There are several options to set up CI for Android. The most widely used are Jenkins, TeamCity, and Travis CI. Jenkins has the biggest ecosystem, with around a thousand available plugins. It is also an open source effort with a lot of contributors. TeamCity is a product from JetBrains, the company that also created IntelliJ IDEA. Travis CI is a relatively new player, and is mostly focused on open source projects...