Prodigal can be an adjective used to describe something as producing or owning a quality or item in overabundance, in other words, lavishly or extravagantly.
A person who is described as prodigal is someone who is extravagant with his or her money or some other resource. This word is always used with the feeling of wastefulness. It can also be a noun, so someone could be a prodigal.
In the Bible this term was used in a parable by Jesus. The story is normally referred to as the prodigal son and was about, oddly enough, a son who wasted his inheritance and came back home repentant and penniless. When someone is either making bad choices or coming back home repentant, he or she can be termed a prodigal son or daughter.
The noun form can be prodigality, and the adverb is prodigally.
Prodigal comes from the Latin word prodigus or lavish, which incidentally is not the root for the word prodigious.
Prodigious, which means to be inordinately large or remarkable in some way, comes from the same root as prodigy. The root is prodigium, the Latin word for portent or omen, something out of the ordinary and very special.
As a note, the adverb form of prodigious is prodigiously and is usually used to modify other modifiers. The noun form is prodigiousness.
Prodigy is a term used for someone with extreme and highly unusual talent in a specific area. It is usually used with a modifier. Someone can be a piano prodigy or a math prodigy. While the word can be used rather loosely sometimes, actual prodigies are very rare.