In simple terms, Torrent files are small files (<100 KB) which contain metadata (index of files which you desire) which is read by your torrent client after which the data (that you desire) is sent to you through seeders. As the desired filed is downloaded, the client will also act as a seeder and share parts of the file to other peers. Since the client is both uploading and downloading, it is strongly recommended that a VPN be used to protect your IP address and privacy if you live in an area where digital copyrights laws are strictly enforced.
Should I use a free VPN? No. Free VPNs are likely to collect data from you for marketing purposes, be too slow to bother with, or do not allow torrent traffic in the first place. It's recommended to purchase a subscription of a VPN service - many can be as cheap as 3 USD/month, if you buy in bulk.
Trackers: A tracker is a website that helps peers find each other, by hosting the torrent files in a searchable interface. There are many private and public trackers. Public trackers are easy to access but have a greater risk of infected files and being monitored by copyright enforcers. Private trackers tend to have higher quality files, are less risky, but are harder to get access to and typically have strict guidelines for users.
VPN: Stands for Virtual Private Network. When you switch on a VPN, it sends your web traffic through an encrypted tunnel to a server controlled by the VPN company. From there, it exits onto the web as normal. If you make sure to only connect to websites secured with HTTPS, your data will continue to be encrypted even after it leaves the VPN. This sounds simple, and maybe superfluous, but it can have profound effects on your privacy. When your VPN is on, anyone snooping on the same network as you won't be able to see what you're up to. This is true even if the snooper controls the network, like your Internet Service Provider.
Client: This is the program you need to run torrent files. There are many different clients you can use but qBittorrent and Deluge are two good lightweight and ad-free clients that are very popular and are highly recommended.
Seeders: People who already have the files downloaded on their machines and are uploading them to your computer in real time!
Leechers: People who downloaded the files and left without seeding it, this is considered bad behavior since you're not giving back anything to the community who helped you. It's a good practice to seed to a ratio of at least 2:1... However if you can't seed due to Internet restrictions, then don't. In some countries, downloading copyrighted material is not illegal but uploading it is so make sure to educate yourself on your country's piracy laws (Ask the all-knowing duck at duckduckgo.com)
Peers: This is the total number of people who are connected to the torrent swarm. These include all those who are currently downloading and/or uploading files. In mathematical terms: Seeders+Leachers=Peers.