Many companies offer LAMP hosting, but some of the cheaper LAMP providers do not allow SSH access, reserving that feature for higher-paying customers. Without SSH you may think you'll have trouble executing commands on the hosted server. Not so -- PHP Shell allows execution of some commands without having SSH access to the LAMP server.
The only PHP function that PHP Shell requires is
proc_open(). If you can execute that function using PHP code, then PHP Shell should work. As PHP Shell is easy to install, the easiest way to find out if you are allowed to execute it is to just install it and see if it runs.
You might wonder about the security of setting up a PHP script that allows shell commands to be executed, but PHP Shell is no more or less secure an application than any other PHP file on the server. Of course, you must be responsible for your own security.