Filesystems, Disks and Memory

could anyone Explain me with how the linux o/s keeps track of file
updates in network environment? for example, assume that more than one
computer is connected to network (with linux in all of them). if an
user say 'X' logged into terminal 1 and created a file with the name
of 'temp.txt'. The file would be stored in his computer's local hard
disk. right? then, how come the 'temp.txt' file would still be
accessible if user 'X' logs on to different terminal say terminal 2
(Eventhough it doesn't have file 'temp.txt' in it's local
harddisk)?? . Assume that we are not doing any explicit transfer of
file.

any help with my problem will be greatly appreciated..

Looks like an NFS exported folder, ask your local system administrator, probably he/she has more details.