Splitting the database and putting a copy of the front end on each user's PC is one of the rules for multi-user environments. Have a look at the Ten Commandments thread.
By not splitting your database, it's just a matter of time until something becomes corrupt.
To answer your question about why only one user can access the database at a time: When I came to work at my present job, there was a DB on the network that was not split. When one user had the DB open, the others could not double-click on the file to open it.
BUT... you could open Access, then use "FILE" --> "OPEN" browse for the file, and open it that way. I'm not 100% sure why it worked this way, but maybe your situation is similar.
That was the very first thing I fixed... I split the DB and gave each user a copy of the FE.
Craig