Inevitably, as you research new technologies, your older ship designs will become relatively less and less effective. To keep the list of possible designs relatively short when issuing production orders, there are two things you can do to outdated designs.
First of all, your custom designs are saved in a file, and the same design will be available to you in a different game should you research all the prerequisite technologies. Also, the game comes with some "core" designs, which become available as your research progresses.
If a ship becomes no longer useful, you can either Obsolete or Delete it. Obsoleting the ship removes it from the build orders list for all your shipyards, and asks you if you wish to scrap all existing ships of that class. Unless you are severely hurting for cash or have a very large navy, the answer to that latter question is generally no - it's better to keep slightly obsolete ships to inflate your power ranking and to use for defense. Also, a very experienced older ship may have high hit points, and may warrant paying the money to upgrade it to a newer design. An obsolete design will still be available in all other games once the necessary techs are researched.
Alternatively, you may chose to Delete an old ship. This is equivalent to obsoleting, except that it permanently deletes the file to which the design was saved. That means that this particular ship will no longer be available in other games. Notice that "core" designs cannot be deleted, they can only be made obsolete.
WATCH OUT! you might accidently click on Obsolete and your ship will disappear without even an "Are You Sure?" screen.