If John T's answer was what you wanted, then you mis-stated the question :)
He's succinctly described the < and > operators, but you asked about <>. This is a rarely used operator which I'm not sure I'd expect to see in LPIC-1, but just for the record (given that you've probably done with that exam by now):
When you run interactively a command without redirection its standard input, output and error will normally be attached to the tty; it will read from stdin and write to stdout/stderr. Though you might not expect it, those file descriptors are typically opened read-write. Try running a script like
echo "I'm writing to stdin!" >&0
Running this bare will work, at least in current bash versions. However, when you use the < and > redirectors, the stdin and stdout file descriptors are only opened for read and write respectively, so if you invoke this with input redirected from a file -
./write-to-stdin < /tmp/some-input
it won't work (reasonably enough). If you really want a program you invoke with redirection to be able to write and write to a single file descriptor, <> will do the job.
./read-and-write-stdin <> /tmp/some-input-and-output
./read-and-write-stdout 1<> /tmp/some-input-and-output
As most programs only expect stdin to be a read descriptor and stdout to be a write descriptor, you can probably see why this is rather rarely useful, but if you're writing subordinate scripts (or using functions) you can take advantage of the behaviour yourself.