TL;DR

Make sure to back up both your picture files, and your Lightroom catalogue. Both are important if you want to keep your pictures and the edits you made to them.

Details

Lightroom itself does not pack a full backup solution unfortunately, so you need to take care of that yourself. The two most important things in Lightroom to backup are:

• The catalogue
• The actual Photos

There are a few other minor things, like saved presets for editing and such, but I don't worry about these here.

Catalogue

The catalogue is just a big relational SQLite Database. It contains references (paths) to your actual photo files, and the Edits, Keywords, etc. you applied to them. Most of this information can also be saved to so-called XMP-Sidecar files, but nevertheless, its very important to have a backup of the catalogue. Otherwise, you could end up with a lot of work.

The purpose Catalog-Backup-Feature you mentioned is to have a copy available, if the main one for some reason gets corrupted. In that case, you can open the backup copy and have everything available again.

Photos

Lightroom usually does not touch the actual photo files, and with Smart-Previews you don't even need to have access to the originals to edit them. But nevertheless, you should have multiple copies of your original files available in different locations.

Backup strategy

Now this depends a lot on your setup. If you have your Pictures and your catalogue in one folder, just copy that to your external harddrive (or use some script or tool to automate that), then you should be good to go if your harddrive fails.

With Lightroom it's also possible to have e. g. your older originals on some Network-Drive or NAS and having Smart-Previes. Newer Photos reside on your Laptops' drive - In that case you just need to make sure that you back up every location where Photos are stored.

Just make sure to also back up the catalogue, or you will loose all your edits!