The draw weight of a bow is the pull weight which applies to your fingers on the string while the bow is fully stretched. This weight changes with the length you stretch the bow. So, to compare different bows, the bowyers often refer to 28 inches. This indication often looks like this
50#@28". This basically means that you have to hold 55 pounds (#) if you pull the string 28 inches (") back.
I've already talked about the draw weight a little bit in this question.
The force required to hold the string stationary at full draw is often
used to express the power of a bow, and is known as its draw weight,
It's easy as that, really. It's just the force one needs to apply to pull the bow.
However, you have to hold in mind that this indication doesn't really say something about the bow. It's like someone is saying: "My (not further defined) vehicle has 120 HP." What do you know? Nothing, to be honest. You'll ask the person about the kind of his car and motor. You may also want to know the weight of it and so on.
The same thing applies to bows. First of all the poundage is mostly given for 28" draw length*. This is just a standardization cause every archer has its own draw length depending on his anchor and body size. Refer to it as the 3000 rounds per minute which are used to measure the horse power of a car.
So, let's say an archer is shooting a 35#@28" bow but has a draw length of 26". He is effectively shooting about a little bit over 30 pounds. Just like a 100 HP car driven at 2000 rpm has only about 80 HP or something.
The other thing to hold in mind is that it doesn't have to do anything with the speed of the bow (how fast the arrows fly). This depends on your bowtype (e.g. recurve-bow, longbow, compound-bow), your bow material, your string, your arrows and so on. Just like you don't know anything about the vehicle in the first place. Things just get clearer the more details you get (it's a sports-car, it weights x kg ...).
The maximum distance the string could be displaced and thus the
longest arrow that could be loosed from it, a bow’s draw length, is
determined by the size of the archer.