What is Entry Processes?
What we should know about the limitation of the Entry Processes is that they limit the control numbers of all entries into the LVE (Lightweight Virtual Environment). Every single time a process "enters" into the Lightweight Virtual Environment, the counter is incremented. You can also see it as a term "Apache concurrent connections" limit/s. It is important to know that the process created inside the LVE are not counted.
Basically one process enters into LVE once a new HTTP for PHP/CGI is made.
The idea of this limitation is to prevent the server from DoS attacks. One of the most popular attacks is by hitting a slow page on the web server by making a lot of Apache connections. When this happens all the slots that Apache has are used and no one else can be able to reach the server, showing him "can not establish connection", white screen and so on. And here comes the CPU limits. Once the website stats to get slower and slower due to CPU limits, the responses are getting slower, causing more and more connections to be tied up.
In order to get rid of that, CloudLinux created the entry processes limit. You can also see it as concurrent connections limits. It;s job is to limit the number of concurrent connections to Apache, avoiding web server to serve error 508 page - in other words Resource Limit Reached. The limitation runs till the number of concurrent requests for the site goes above the limit.
NPROC from coreutils prints the number of processors. It also takes main part of controlling the total number of processes and threads within LVE. Once the given limit is reached, no new process can be created (until another one dies and leave a slot to the new one). If this happens NPROC counter is incremented and in Apache return 500 or 503 errors on a white page.