Upside is another word for potential. If a player has great upside, he has the inherent ability to raise his game to another level. Often times, young players haven't filled out their frame or matured enough in a physical way to maximize the talent that they possess. Often times the conotation of this word is a direct result of a player who "hasn't put it together", at the highest level. Usually, the player has been seen to have star quality but is just inches away from realizing it. If a player has high upside, there is a lot of room for improvement from where his current game is and where it could possibly end up. If a player has low upside, he has nearly maximized the potential he has to be a productive player. A "safe bet", if you will. You know what you're getting.
Evidence of this can be seen as recently as the 2003 NHL Draft. The New York Rangers selected Hugh Jessimen with their 1st Round selection. This wasn't because Jessimen's talent level demanded he go so high, it was because he was percieved to have "high upside". The particular reason that the scouts saw potential in Jessiman was his size. At 6'6 240, Jessiman had the body of a powerforward at the ripe young age of 18. Despite other inconsistancies in his game, the Rangers scouts saw the potential to hit a home run with this type of selection. His upside was high, but his risk was high as well. Upside and Risk are almost synomous in most cases. That is due to the fact that taking a more established player is less risky, but taking what's behind door #2 occasionally ends up being the better reward.
Teams that live by the "upside" also die by it. Teams that draft players on this alone often end up with a track record that is mostly hit or miss. While teams who tend to draft in a more conservative way tend to have less great draft selections and more solid contributers. The key to drafting is to find the happy medium between taking chances and the sure thing. Nobody is able to perfect it, because there is no accurate way to judge the future development of a player. That is why in almost every draft you'll find that a player taken in the top 15 selections didn't get there on merit alone.