Parallel means two (or more) items that both perform a particular task at the same time. For example, a truck might have dual tires, so that if one fails, the truck can still operate - perhaps not quite at 100%, but well enough to get by until repairs can be made.
You can also have standby components or systems. For example, an emergency generator for a hospital. This systems only kicks in when there is a failure in the primary system. The space shuttle has - I believe - 5 computers! to manage key tasks. Even if 4 of them fail, the fifth can still handle the task.
Both of these set-ups would be considered redundant, since they are not needed as long as things are working properly.
Tim
P.S. I moved & merged the posts from two other threads. I don't see any forum specifically for reliability, but this seemed like a good choice.