When an Access app is opened a locking file is created that keeps track of all users. This locking file performs several functions including record locking. The limit on concurrent users is in this file. So there can only be 255 users currently logged in at the same time.
Since a multi-user Access app should be split between a local front end and a shared back end, it is only the back end where the number of logged in users is a concern. Frankly, you will probably encounter performance issues before you reach the 255 limit. It would be a rare Access app that would have 255 people logged in and working with data at the same time.
The solution, though, is to store your data in a different database engine then the native Access data store. SQL Server is an alternative.