Question
What is the true definition of a weed? Is it a clasification of a type of plant or can anything that is deemed to be unwanted be called a weed?

Answer
Any plant which is growing where it is not wanted could be classified as a weed.  This is the broadest definition.  

Plants most commonly defined as weeds tend to have certain characteristics in common: they produce prodigious amounts of seed, their seed remains viable for many years, they have a very short reproductive cycle, they thrive in a wide variety of situations, and many also rapidly spread underground by means of stolons, which are fragile and tend to grow a new plant out of the smallest fragment remaining.