Either (1) a specific server environment, or (2) the process of combining disparate systems at the code level.
Sometimes synonymous with a testing environment, though integration servers tend to see a lot of new code. Every time a developer submits code to the the source code management system, that code will likely be deployed to integration. This code will be raw and untested for even basic execution. As such, there might be a separate testing server to which more mature code is deployed less frequently.
As a verb, to “integrate” software is to make disparate systems work together at some level. For instance, the process of allowing your CMS to push data into your new release management system would be to "integrate" the two systems. Integrations are often packaged and sold as connectors.