SSL accelerator is a component, which terminates SSL connection. In the infrastructure behind the accelerator, the communication is unencrypted.
A typical usecase is Nginx as reverse proxy, which terminates SSL connections. Behind it runs an Apache server (executing PHP for example). The communication between Nginx and Apache is unencrypted. An application recognizes that it is running over HTTPS from the X-Forwarded-Proto header. The application must check this header, or it might not work correctly.
Another usage scenario are clusters, where load balancer acts as an SSL accelerator.
If your application is compatible with using an SSL accelerator, we would recommend using it, especially on high traffic websites. It prevents encryption within the internal infrastructure, thus improving performance.