We have the license of ArcGIS 10 for concurrent use. For the data security and validation, we installed the application in a remote server, where we are a group of three people can access the remote server concurrently. But, the problem is we can use the ArcGIS only one person at a time, whether we have the concurrent license. How can we three people concurrently use the ArcGIS 10?
You seem to have misunderstood the meaning of "concurrent" in the Esri licensing documentation.
Concurrent use is defined:
This is a license environment where core products and extensions on client machines obtain and share licenses from a pool of available licenses that reside on a networked license manager.
which is distinct from Single use
This license environment is where licenses for core products and extensions are authorized locally on the end-user machine.
Whether you choose concurrent use or single use licensing, you would still need three licenses for three users utilizing the software at the same moment.
The difference occurs when you have an office of a dozen potential users, any three of whom need to use a license at one time. The "floating seat" of concurrent licensing allows all users to have the software installed, and they "check out" a seat from the license server on a "first come, first served" basis, whereas the single use model would require licensing twelve seats for the same pool of users.