The Ship of Theseus Paradox posses the question that if enough of an original object is replaced, does that object remain the same or has it become something new.
The origin of this paradox is also where it got it's name. The ship of the Greek hero Theseus was used as a memorial and in religious missions to Delos to honor the god of light and sun, Apollo for years after Theseus' passing. In order to keep the ship in seafaring condition, wooded that rotted or worn had to be constantly replaced. So much so was the extent of this repair and replacement that philosophers questioned if the ship was still the same as the one Theseus used in his lifetime.
Now the Paradox refers to both any vessel or vehicle but also object in general that extensive repair and replacement happens too, but is often associated with ships due to its origin.
The main idea presented by the paradox is one of identity and whether or not something can remain the same despite undergoing change. Arguments regarding this have incorporated the similar paradox of “stepping into the same river twice”, which has been deemed by many philosophers to be impossible due to the constantly changing nature of the river due to the flowing of its waters. The use of this argument in conjunction with the Ship of Theseus Paradox would suggest that it does not remain the same.
On it's most basic level, the paradox questions whether or not it can still be named the same thing. On a deeper level, it questions the identity of the object can be considered the same on multiple levels, including, but not limited too, name and distinguishing characteristics.
For further reading, consult: http://en.wikipedia.org/wiki/Ship_of_Theseus