Concurrent Connection:

The number of authenticated "handshakes" between a client and/or server during any given time before all communications have been disconnected whether by force or by refusal. In layman's terms : "how many people are using your website or calling a task at one time."

Scenario of Concurrent Connection:

e.g. if visitors click to read a thread in your forum, then a post in that thread, that is 2 connections, but they are one at a time.

or another scenario;

If you have 10 people who click to read any post at the same time, (not the same post), that is 10 concurrent connections. As each one finishes, and the page is loaded, that connection is closed.

Solution:
The only method to increase the limit of concurrent connections is to upgrade your hosting. If you do not do this it may overload our current hardware server platform e.g VPS or Shared Hosting hardware node.