Yes, AWeber has a full featured API, allowing users to easily connect their AWeber accounts with other sites and services online. AWeber users generally don't need to interact with the API directly - you can simply use one of the many hundreds of existing integrations that developers have already created.
For instance, to use the AWeber Webform Widget for Wordpress, you just install the plugin on your Wordpress site and use it from within your Wordpress control panel.
Authorizing integrations designed to work with AWeber should be explained by the site or person that provided that integration. Learn how you can authorize a new integration.
As with connecting integrations, deactivating them will mostly be a matter of either changing the settings of the integration on the site that offered it to you in the first place, or simply uninstalling the integration. Learn how to remove or delete an integration.
The Integrations Showcase
If you click the "Integrations" link in the upper right of your AWeber account, you'll be taken to the "Integrations Showcase."
Here you will see a searchable directory of hundreds of different available integrations in a variety of categories. After clicking on any integration listed, a brief description is provided as well as a "Connect Integration" button allowing you to start using the integration.