Entry processes limit control the number of entries into LVE. Each time a process 'enters' into LVE, we increment the counter. Each time process exits LVE, we decrement the counter. We don't count processes that are created inside LVE itself. It is also know as 'Apache concurrent connections' limit.
The process enter's into LVE when there is a new HTTP request for CGI/PHP.
This limit was created to prevent DoS attacks against web server. One of the fairly popular attacks is to tie up all the Apache connections by hitting some slow page on a server. Once all Apache slots are used up, no one else will be able to connect to the web server, causing it to appear to be down. The issue is worsened by CPU limits, as once site starts to get slow due to CPU limit -- it will respond to requests slower and slower, causing more and more connections to be tied up.
To solve that, we have created entry processes (often called concurrent connections) limit. It will limit the number of concurrent connections to Apache, causing web server to serve error 508 page (Resource Limit Reached), once there number of concurrent requests for the site goes above the limit.