ContentDB
The Content DB is the official source to download mods, games and texture packs that have been developed by the Minetest community. It's the fastest and most convenient method to obtain those things.
The Content DB can be accessed in Minetest (“Content” tab) or with your browser via content.minetest.net.
Usage
In Minetest
(You need Minetest 5.0.0 or later.)
In the main menu, click on the “Content” tab. You will see a list of everything that you have already installed.
To get to the Content DB, click on “Browse Online Content”. You will see a list of all available mods,
Here you can browse and directly download and install the things you like to install. Everything you download here will be available instantly, once it's installed. No restart required.
Use the drop-down list in the top right corner to filter the content type.
Note that mods and games might receive updates by their respective authors. If an update is available, you can simply return to the Content DB and click on “Update”.
And that's really all there is to it!
The website
The website of the Content DB is at content.minetest.net.
The main advantage of the website is that it contains more information to read, more screenshots to admire and more links to click on. You can also download the stuff from here as well, but then you need to manually install it to the correct location, of course. See Mods, Games or Texture Packs to learn more.
On software freedom
Proprietary software, or things under restrictive license terms in general, are currently NOT banned on the Content DB. But they are currently (as of 5.2.0) being hidden by default in Minetest.
This means that everything you can download from Minetest's Content tab is released under a free/libre license. But on the Content DB website, you might run across proprietary things. Those things that are under restrictive licenses are always explicitly marked as such.
Please note that almost every contributor in the Minetest community contributes their things under free/libre software licenses. Proprietary software is a rare sight and even then, it's generally frowned upon.