Right here homie.
Several people here have gotten it right, but just to confirm: a contract is an agreement between two or more parties for valid consideration. There must be 1. offer and acceptance, 2. an intention to be legally bound by the terms of the contract, and 3. valid consideration.
Here is an example of a valid contract: Two guys at a bar. "Hey Joe, still have your F150? It's a 1998, right? I'll buy it for $2000". "Sure Bob, you've got yourself a deal."
So there are a couple of elements.
First, you need an agreement. The fancy latin is "consensus ad idem" which translates to a "meeting of the minds" - both of you need to be on basically the same page as to what you're agreeing to. Consequently, a contract can fail for certainty of key terms, like, say, the price you're buying a truck for. If I think I'm buying your Ford F150 for $1000 and you think you've agreed to sell it for $1500, we don't have a contract. Similarly, if I think I'm buying your 1998 F150 and you think you're selling your 2004 version, we don't have a contract. That should be obvious - but the degree to which certain terms are "key" can vary. For example, in the above example we didn't set out when Bob gets to pick up the truck. Let's say he thinks he can come get it tonight, but Joe can't give it to him until the weekend for whatever reason. That may or may not be important enough to invalidate an agreement, which is why when they're written down you see terms like "time shall be of the essence in this agreement". This is also where capacity comes in - a person who doesn't have capacity to enter into a contract can't form the requisite consensus ad idem (say they're senile or eight years old or whatnot).
The "intention to be bound" is generally assumed in a situation like a purchase and sale. But let's say your mom promises to give you a hundred dollars if you clean your room every week for a year, and at the end, she decides she's not going to. You can't sue her. That was a domestic situation and while she's being a bit of a bitch, the Courts don't want to deal with that nonsense. Also applies in situations where advertisers make crazy claims that are clearly not serious and someone decides to treat them like they're a term of a contract or something (there's an old case about some weird cold and flu remedy or something that calls these "mere puffs" of advertising). But usually this isn't an issue.
"Consideration" is the stuff you get under the contract. In my example, it's the truck and the money. Joe gets the money, Bob gets the truck, both are valid consideration. There can be situations where you have invalid consideration; for example, let's say Bob said "Hey joe, all that work I just did for you re-painting your house, I should get your old truck for that right?" and Joe agrees. That's not a contract, because the consideration is "past" - if Bob had said before painting the house that he wanted the truck in exchange for doing it, that's no problem; services provided for a fee in money or property is all fine. But because they didn't purport to form the contract until after, it's not, legally, a contract.
Then there are lots of things that can invalidate or void an otherwise legal contract, like illegality, unconscionability, duress, misrepresentation etc. etc. But those merely invalidate a contract - there's still a contract there.
"So what's all this bullshit about signing shit then, JD?"
Glad you asked because I love dispelling this myth. It seems that the majority of the population is so mystified by law that they treat it like some sort of alchemy. Within that perspective it somehow makes sense that signing a piece of paper is like wielding a magic wand, or something, and when you write your name on that piece of paper it has MAGICAL LEGAL CONSEQUENCES! So if you read nothing else in this post, remember this:
A signed piece of paper is not a contract. It is only EVIDENCE of a contract.
It is supposed to be used later to look at and say, "hey, what did we agree to? When was I supposed to pick your truck up? Did it come with the tires? What if it breaks down in the first 1000km, did we address that in our agreement?" Writing this all out ensures that everyone knows what's being agreed to, and in the event that you disagree, you can go to court, show it to the judge, say, "Hey judge, here's what we agreed to, and the fact that we agreed to it is EVIDENCED by those two signatures on it". That is ALL that the piece of paper and the signatures are for. Nothing else. They do not create a legal relationship, they don't create a contract, the contract is just the AGREEMENT between you two, which you can have with or without a signed piece of paper setting out the details.
So there's your primer on contracts!
