CLR_MONITOR is one of the wait types in SQL Server 2008. It occurs when a task is currently performing CLR execution and is waiting to obtain a lock on the monitor according to BOL. When this shows up in sys.dm_exec_requests, it means the session is running a CLR which is waiting for lock being granted to an object by using Monitor class.

static class StaticVariables
{
    public static object SyncObj = new object();
}
[Microsoft.SqlServer.Server.SqlFunction]
public static SqlInt32 Wait10Sec()
{
    lock (StaticVariables.SyncObj)
    {
        Thread.Sleep(10000);
        return new SqlInt32(1);
    }
}
[Microsoft.SqlServer.Server.SqlFunction]
public static SqlInt32 Wait10Sec_1()
{
    try
    {
        Monitor.Enter(StaticVariables.SyncObj);
        Thread.Sleep(10000);
        return new SqlInt32(1);
    }
    finally
    {
        Monitor.Exit(StaticVariables.SyncObj);
    }
}

Look at the code above, I created 2 CLR functions. The first one waits for 10 seconds after locking a static object member in an static class. The second function is same as the first one but using Monitor class.

--first window in SSMS, (spid = 55)
select dbo.Wait10Sec()

--second window in SSMS, (spid = 58)
select dbo.Wait10Sec()

--thrid window, it's monitor window.
select  session_id, wait_type, wait_time from sys.dm_exec_requests where session_id = 58

Run the script in the first window(spid = 55) then run the script in the second window (spid = 58) then run the script in the third window:

session_id wait_type      wait_time
---------- -------------- -----------
58         CLR_MONITOR    4005

(1 row(s) affected)

If you change the function call in the first and second window to dbo.Wait10Sec_1(), you should get the same wait type from the DMV.