API Certificates are used to authenticate you to PayPal APIs. If your Certificate expires, PayPal can't authenticate you as a valid API user. As a result, you won't be able to process any transactions via the APIs. If your Certificate has expired, you can renew or change your API Signature or Certificate credentials.
Visit Create and Manage NVP/SOAP API Credentials for detailed instructions.
See also:
What are API Signature and Certificate credentials?
PayPal NVP and SOAP Reference Guides