Trying to understand which parameters I need for a generic backup using rsync
 

Simply trying to backup a directory to external hard drive; I came across a tutorial which used the -av parameters, which should be sufficient for what I want to do? I came across also the concept of hard links using -H but I'm unclear on what that does or whether I even need it, my inclination is to think not.

If the directory has subdirectories, you might want -r. My understanding is that -H is usually used when you want to make a bootable copy of your disk.

The options -av should be sufficient.

If you were using hardlinks you'd probably remember setting them. Though one place that rsync can make use of hardlinks is in doing incremental backups. See the --link-dest option if you are interested in planning incremental backups.

>>>If the directory has subdirectories, you might want -r

archive mode -a already includes -r for recursion

-a, --archive archive mode; equals -rlptgoD (no -H,-A,-X)

>>>My understanding is that -H is usually used when you want to make a bootable copy of your disk.

Hard links have nothing to do with booting which relates to a disk's MBR. You would use dd to copy the MBR.