Most mature projects maintain multiple release lines in parallel. For example, after 1.0.0 comes out, that line should continue with micro (bugfix) releases 1.0.1, 1.0.2, etc., until the project explicitly decides to end the line. Note that merely releasing 1.1.0 is not sufficient reason to end the 1.0.x line. For example, some users make it a policy never to upgrade to the first release in a new minor or major series—they let others shake the bugs out of, say 1.1.0, and wait until 1.1.1. This isn't necessarily selfish (remember, they're forgoing the bugfixes and new features too); it's just that, for whatever reason, they've decided to be very careful with upgrades. Accordingly, if the project learns of a major bug in 1.0.3 right before it's about to release 1.1.0, it would be a bit severe to just put the bugfix in 1.1.0 and tell all the old 1.0.x users they should upgrade. Why not release both 1.1.0 and 1.0.4, so everyone can be happy?
After the 1.1.x line is well under way, you can declare 1.0.x to be at end of life. This should be announced officially. The announcement could stand alone, or it could be mentioned as part of a 1.1.x release announcement; however you do it, users need to know that the old line is being phased out, so they can make upgrade decisions accordingly.
Some projects set a window of time during which they pledge to support the previous release line. In an open source context, "support" means accepting bug reports against that line, and making maintenance releases when significant bugs are found. Other projects don't give a definite amount of time, but watch incoming bug reports to gauge how many people are still using the older line. When the percentage drops below a certain point, they declare end of life for the line and stop supporting it.
For each release, make sure to have a target version or target milestone available in the bug tracker, so people filing bugs will be able to do so against the proper release. Don't forget to also have a target called "development" or "latest" for the most recent development sources, since some people—not only active developers—will often stay ahead of the official releases.
A security release is a release made solely to close a security vulnerability. The code that fixes the bug cannot be made public until the release is available, which means not only that the fixes cannot be committed to the repository until the day of the release, but also that the release cannot be publicly tested before it goes out the door. Obviously, the developers can examine the fix among themselves, and test the release privately, but widespread real-world testing is not possible.
Because of this lack of testing, a security release should always consist of some existing release plus the fixes for the security bug, with no other changes. This is because the more changes you ship without testing, the more likely that one of them will cause a new bug, perhaps even a new security bug! This conservatism is also friendly to administrators who may need to deploy the security fix, but whose upgrade policy prefers that they not deploy any other changes at the same time.
Making a security release sometimes involves some minor deception. For example, the project may have been working on a 1.1.3 release, with certain bug fixes to 1.1.2 already publicly declared, when a security report comes in. Naturally, the developers cannot talk about the security problem until they make the fix available; until then, they must continue to talk publicly as though 1.1.3 will be what it's always been planned to be. But when 1.1.3 actually comes out, it will differ from 1.1.2 only in the security fixes, and all those other fixes will have been deferred to 1.1.4 (which, of course, will now also contain the security fix, as will all other future releases).
You could add an extra component to an existing release to indicate that it contains security changes only. For example, people would be able to tell just from the numbers that 18.104.22.168 is a security release against 1.1.2, and they would know that any release "higher" than that (e.g., 1.1.3, 1.2.0, etc.) contains the same security fixes. For those in the know, this system conveys a lot of information. On the other hand, for those not following the project closely, it can be a bit confusing to see a three-component release number most of the time with an occasional four-component one thrown in seemingly at random. Most projects I've looked at choose consistency and simply use the next regularly scheduled number for security releases, even when it means shifting other planned releases by one.