This is a very good question – answer set on StackOverflow. It considers situations, as well as the technical issues. And, it points out where the idea of a “key” fails. But, first, you may be wondering what public and private keys are, and why they matter.
What is a Public Key
The image of the lock has a key to open it. Depending on what type of lock it is, you may need the key to lock it, or you may be able just to push the post down into the hole and lock it without a key. If you can just push the post down into the hole, locking it is public, anyone can do it. If you need a key to lock it, both the locking and unlocking are private actions.
The second answer is interesting because it goes into the math.
For information on the difference between symetric and asymetric: