Why is the SOAP API being removed?

The SOAP and XML-RPC APIs were deprecated in February 2013 and have been replaced in JIRA 7 by a complete REST API.

Am I going to need to make any changes in order to avoid being affected by the removal of these APIs?

The two largest software products known to use this API are Zephyr Enterprise Edition and the JIRA Command Line Interface from Appfire. These are both going to have an update out in time for the removal of the APIs.

Other possibilities include custom Jenkins or other CI scripts, and any other sort of in-house script that pulls or pushes data to JIRA via the SOAP or XML-RPC APIs. Those scripts will need to be migrated to use the REST API in order to keep working.

Unfortunately Atlassian is unable to identify the source of the API calls, identifying the source and updating custom scripts or add-ons will need to be performed by the administrators of the Application.

I know I'm using custom scripts, what changes do I need to make?

We've put together a guide showing which SOAP/XML-RPC calls correspond to which REST calls in the JIRA SOAP to REST Migration Guide. The REST API documentation itself can be found at the JIRA REST API Reference.