Any operating system has processes (p's) running, say p1, p2, p3 and so forth. Each process usually makes an ongoing usage of files.
Each process is consisted of a process tree (or a process table, in another phrasing).
Usually, Operating systems represent each file in each process by a number (that is to say, in each process tree/table).
The first file used in the process is file0, second is file1, third is file2, and so forth.
Any such number is a file descriptor.
File descriptors are usually integers (0, 1, 2 and not 0.5, 1.5, 2.5).
Given we often describe processes as "process-tables", and given that tables has rows (entries) we can say that the file descriptor cell in each entry, uses to represent the whole entry.
In a similar way, when you open a network socket, it has a socket descriptor.
In some operating systems, you can run out of file descriptors, but such case is extremely rare, and the average computer user shouldn't worry from that.
File descriptors might be global (process A starts in say 0, and ends say in 1 ; Process B starts say in 2, and ends say in 3) and so forth, but as far as I know, usually in modern operating systems, file descriptors are not global, and are actually process-specific (process A starts in say 0 and ends say in 5, while process B starts in 0 and ends say in 10).