A naked position is when one has a non-hedged position. It can also refer to some option positions.
This term is not as well known as some others. It refers to not being covered against risk that the price of a security will move one way or the other, depending on what type of position you have.
For instance, if you have a long position without an offsetting short position, you are considered to have a "naked" long position. That is, you are naked to the risk of seeing the price of your long position decline, leading to a loss. If you had hedged that position with some sort of short, maybe going short in a different company in the same industry, your long position would be "covered." For instance, if you are long in shares of Ford, you would be naked unless you shorted some other automaker, such as General Motors.
Similarly, you can also be naked on the short side.
With options, you are naked if you have sold a call without owning the underlying shares. You are also naked if you have bought a put without owning shares of the underlying security.
For most individual investors, being naked is not a concern. Unless you are outside in a snowstorm, of course. However, for many institutional investors, being naked can be a major concern.