Is lemonade better when made with simple syrup?
Simple Syrup is sugar that is has been dissolved in water. Heating speeds the process, and also allows the water to "absorb" more sugar. I don't remember the chemistry of why the sugar doesn't crystallize at room temp, but it doesn't. It is typically made in a 1:1 mixture .. heat a cup of water to boiling, add a cup of sugar, stir until the sugar is dissolved, remove from heat, allow to cool.  

It is used in cold drinks like lemonade and iced tea because granulated sugar does not dissolve easily in cold liquids. It requires a lot of mixing, and the saturation point is low, so people who like lots of sugar can't get enough to dissolve to get the taste they desire.

Note #1: this is why Southern-style Sweet Tea is sweetened while the tea is still hot.

Note #2: The sweetness of 1 tsp of sugar is not equivalent to the sweetness of 1 tsp of simple syrup.  You will have to find your particular taste point.

Note #3: It can be flavored with just about any flavor extract, such as lemon, orange, peppermint, vanilla, almond, and so on. As I understand it, this is typically how flavored iced teas are made.