What does the < (left chevron / triangle bracket) do?

The operator < is most commonly used to redirect file contents. For example

grep "something" < /path/to/input.file > /path/to/output.file 

This would grep the contents of input.file, outputting lines containing "something" to output.file

It is not a full 'inverse' operator of the > operator, but it is in a limited sense with respect to files.

For a really good and brief description, along with other applications of < see io redirection

Update: to answer your question in the comments here is how you can work with file descriptors with bash using the < operator:

You can add additional inputs and/or outputs beyond stdin (0), stdout (1) and stderr (2) to a bash environment, which is sometimes more convenient than constantly switching where you are redirecting output. The #'s in the () next to the 3 'std' inputs/outputs in bash are their 'file descriptors' although they are rarely referred to in that way in bash - more often in C, but even then there are constants defined which abstract things away from those numbers, e.g. STDOUT_FILENO is defined as 1 in unistd.h - or stdlib.h...

Lets say you have a script that is already using stdin and stdout for interfacing with a user's terminal. You can then open additional files for reading, writing, or both, without impacting the stdin / stdout streams. Here's a simple example; basically the same type of material that was in the tldp.org link above.

#!/bin/bash -
#open a file for reading, assign it FD 3
exec 3</path/to/input.file
#open another file for writing, assign it FD 4
exec 4>/path/to/output.file
#and a third, for reading and writing, with FD 6 (it's not recommended to use FD 5)
exec 6<>/path/to/inputoutput.file

#Now we can read stuff in from 3 places - FD 0 - stdin; FD 3; input.file and FD 6, inputoutput.file
# and write to 4 streams - stdout, FD 1, stderr, FD 2, output.file, FD 4 and inputoutput.file, FD 6

# search for "something" in file 3 and put the number found in file 4
grep -c "something" <&3 >&4

# count the number of times "thisword" is in file 6, and append that number to file 6
grep -c "thisword" <&6 >>&6

# redirect stderr to file 3 for rest of script
exec 2>>&3

#close the files
3<&-
4<&-
6<&-
# also - there was no use of cat in this example. I'm now a UUOC convert.

I hope it makes more sense now - you really have to play around with it a bit for it to sink. Just remember the POSIX mantra - everything is a file. So when people say that < is really only applicable on files, its not that limiting an issue in Linux / Unix; if something isn't a file, you can easily make it look and act like one.

It redirects the file after < to stdin of the program before <.

foo < bar

will run the program foo using the file bar as its stdin.