Think of Harvesting as quite simply picking your fruit and the bud is your fruit.
When you start doing a little more searching, reading and asking questions you will find that harvesting at different stages of ripening will give the buds you smoke a slightly different character. For example you could have two different plants same strain, like OG, you harvest one a little on the earlier side and may find that the high is more speedy or energetic in nature, while the one you let go a bit longer might be much more of a couch-lock high.
With curing, think of it as letting your fruit ripen and develop it's character or canning like a jam or jelly. The buds you pick will need to be dried before you smoke it. The most common method, is to dry then cure in jars, mason jars usually but as long as you can get it air tight that is the idea. You dry the buds to a point that they are spongy, they CAN be smoked, but they will most likely have a rougher smoke and have a grassy smell and flavor from the chlorophyl still being there. This is why the canning or jarring; you put them in the jar and allow the chemical breakdown of the chlorophyl to take place, opening the jars and letting these chemicals to air out for a little while before closing it again, this is commonly refereed to as burping. The longer you let this take place (within reason, up to a year from what I have found but maybe longer maybe a little less) the smoother and better flavor and smell you should get. Usually 2-6 weeks is what I have seen people say they do.
Like I said early in this post read a bit more, use the search and glance a little over the FAQ once or twice and you will pick up on this pretty easy, almost ever question you are going to have right now is going to be found there.