Short summary (from memory, so might be a little faulty):
GPLv3 = GPLv2 + you can't sue any users/distributors for violating your patents + you grant an implicit license to all your relevant patents to your users + you must protect users from patents that might be covering code you contribute
For companies with patents and lots of patents they are afraid of losing their ability to sue for patent violations. I'm unclear whether the license you grant is just for the GPLed code or just in general. And in general it's unknown how all this plays out in court, so most lawyers (and thus companies) avoid v3 like the plague.
AGPL = GPL + must distribute even if you just provide an internet accessible service.
The idea being that the GPL only applies to distribution, so if I modify some GPL software but never distribute it (because I just run it on a server I control) I never have to GPL my changes. The AGPL says you have to distribute/open source your changes even if you don't distribute if the modified software is accessible over the network to users.
I think of it as an insurance policy. If I release my server side code as agpl, I know that anyone who uses it also has to share the code in their servers has to share it with their users.
In my simple mind, open source is a developer construct while free software is a user construct. Thank you for bringing a user's perspective in explaining GPL.
FWIW, I tend to substitute the word "user" there, for "software".
I see permissive Open Source licenses as giving developers all the freedom, and copyleft licenses as giving the software itself, all the freedom.
I choose this distinction only because some users are developers, and a copyleft license specifically restricts them from doing some things (i.e. closed source forks), thus restricting their absolute freedom. Instead, the software itself is promoted to the receiver of ultimate freedom, because its basic rights are enforced through all its generations/forks/integrations.
GPLv3 = GPLv2 + you can't sue any users/distributors for violating your patents + you grant an implicit license to all your relevant patents to your users + you must protect users from patents that might be covering code you contribute
For companies with patents and lots of patents they are afraid of losing their ability to sue for patent violations. I'm unclear whether the license you grant is just for the GPLed code or just in general. And in general it's unknown how all this plays out in court, so most lawyers (and thus companies) avoid v3 like the plague.
AGPL = GPL + must distribute even if you just provide an internet accessible service.
The idea being that the GPL only applies to distribution, so if I modify some GPL software but never distribute it (because I just run it on a server I control) I never have to GPL my changes. The AGPL says you have to distribute/open source your changes even if you don't distribute if the modified software is accessible over the network to users.