You can find the available integrations under the Integrations page by navigating to the cog icon in the upper right corner of your project. You need to have at least master permission on the project.
Project services allow you to integrate GitLab with other applications. They are a bit like plugins in that they allow a lot of freedom in adding functionality to GitLab.
Project webhooks allow you to trigger a URL if for example new code is pushed or a new issue is created. You can configure webhooks to listen for specific events like pushes, issues or merge requests. GitLab will send a POST request with data to the webhook URL.