Supply in economics has a slightly different meaning to the word "supply" as it's used in everyday conversation. In the latter, "supply" is most often used as a verb - to provide someone with something. In economics, however, supply is defined as the amount of a good (or a service) that a producer is willing and able to supply across a range of prices.
Just like demand, the supply for a particular good would cover all range of prices. It can be visualised as a table, with each price value having a corresponding amount of goods supplied. If one is referring to the amount supplied for a specific price value, the phrase "quantity supplied" can be used. An important thing to note is that the "price" being referred to is the the price that the good will be sold to the consumer at, not any other price. When the supply is graphed the price is always on the y-axis and the quantity supplied is on the x-axis.
What does a supply graph look like?
When supply is graphed, it will always take the form of a line (or curve) that slopes upwards - that is, the higher the price of the good, the higher the quantity supplied. There are a few reasons for this. Firstly, there's the simple fact that if the good is sold at a higher price then there will be more profit for the supplier. Therefore, they have the incentive to produce a larger quantity of the good because it's more profitable.
The second reason comes from a different viewpoint. Whilst the first reason illustrates the incentive to increase quantity supplied if the price is raised, the second reason says that if the quantity supplied is increased then the price must be raised. This is because the costs of production will increase if there is a higher amount being produced, so the higher price is required to recoup losses.
Finally, the third reason involves a good bit of common sense. As the price for a good rises, other companies will take note of this. As a result, they might move in and start supplying this good as well, which would result in an increased supply along with the increased price.
What would affect the supply of a good?
Since the supply of a good includes the quantity supplied for each price level, something that affects the supply would have to change this quantity supplied for every price. Changing the price so that a greater amount of the good is supplied would not count as a change in supply, because the supply takes into account different quantities supplied at different price levels. This would be a change in the quantity supplied, and an extension in supply (if the quantity supplied increased), or a contraction in supply (if the quantity supplied decreased).
So what would change the overall supply of a good? Well, a change in the costs of production or an improvement in technology are two things. If the costs of production increase, the supply curve will shift to the left, because less can be produced at the same price - and vice-versa. With an improvement in technology, the supply curve will always shift to the right, because technological improvements will cause an increase in the quantity supplied. Another possibility is a change in the climactic conditions - this is especially important for agricultural goods. A drought would mean that less crops would be supplied at each price level.
Sometimes two goods are supplied from one resource, although this is rare. If the price of one of the two goods increases, (remember, the "price" is the price that the good is sold at) then there will be an extension in supply for that good. However, since there is another good that is produced from the same resource, then the supply of that good will increase as well as a side-effect. The typical example here is beef and leather; both of these goods come from cows. If the price of beef goes up, then more cows will be killed to supply more beef to the market. This will also result in an increase in the supply of leather. In short, the increase in price of a complementary producer good, (a good that is created from the same resource) will cause an increase in the supply.
A similar rule applies for joint producer goods. An example of two joint producer goods are wheat and barley: on a farm, these would share the land - they would be produced jointly using the same resources. If the price of wheat increased, there would be an extension in the supply of wheat. This would result in more resources being allocated to the production of wheat, which means that the supply of barley would decrease. In short, an extension in the supply of a joint producer good will lead to the decrease in the supply.
That's it for a basic explanation of supply in economics.