There are a couple different answers to this depending on the circumstances...
Peer to peer downloads (like torrents or filesharing networks)
If you are talking about downloading data illegally (e.g. copyrighted data in many countries), you shouldn't be doing that in the first place. Be a man and download that movie over the normal internet. If you download lots of data this way, you are using up a lot of CPU and bandwidth from multiple servers around the world and basically clogging up the network. That, too, is something you shouldn't do because the network will cease to be possible if too many people do this.
If you need to download lots of data anonymously and you have a real purpose for being anonymous (e.g. you're a journalist writing a piece on child porn), be my guest and use those resources.
If you're someone wanting to play the latest games without paying, well, I think you know where this is going.
Downloads from websites
And you are NOT using https
When connecting over Tor to the open internet (any http:// or ftp:// address), Tor basically works as a proxy server. The website that you download from sends data, a few nodes in the Tor network forward it, and eventually it ends up with you. That is, if everything goes as it should.
What Tor also does is encrypt the traffic inside the Tor network. This means that any MITM attacks on your local network (for example an insecure WiFi network) are not possible. So this is an advantage for using Tor to download things.
On the other hand, you are willingly proxying your traffic through at least one other stranger on the internet that can modify the traffic as desired. That is also a risk to consider, so be sure to validate any checksums if available.
And of course like always, Tor also masks your IP address (and thereby the possibility to find your physical location), which works especially well when you are using the Tails OS or the Tor Browser Bundle.
If you are using https
The only added value of Tor in this case is that it will mask your IP address.
If you are visiting an .onion website and downloading from there
This works much the same as https, except that now it doesn't only mask your IP address, it also masks the server's IP address. Law enforcement and others basically can't monitor that anyone downloaded a file from that server at all. It makes the server anonymous as well as you.
Note that it may technically be possible to unmask people using Tor if someone really wants to spend millions (billions?) on it, but this is usually not the case. If this is a concern, read more about how Tor works, this answer is certainly not sufficient.