Entry processes are the number of processes that enter your account.
For example, every PHP page that is accessed by a visitor will usually generate a single entry process. Many misinterpret this value as “number of visitors you can have on your website at once”. While it is true that each visitor accessing a PHP page will spawn an entry process, these processes typically end so quickly that it is extremely unlikely that 10 will be spawned at a single moment unless you had a significantly large number of simultaneous visitors on your website at once. Keep in mind, cron jobs also count towards entry processes.
If the limit for entry processes is met then further processes will be denied. If you are trying to access a PHP page you will receive a 508 (Resource Limit Reached) page. Once the requests decrease below the limit, the website will stop showing a 508 error.