Let's split it up into a few parts of the year:
1 - Hot, wet and busy season (May through August). This is the time of year that the weather in Cuba is hot, humid and everyone seems to have their shirts off! Consequently, it's the busiest tourism season because it coincides with summer vacation for Europeans, Canadians and American travelers.
2 - Hurricane season (End of August to First of November). You don't want to hear it, but it's true. Hurricanes hit Cuba like any other Caribbean Island so it's a bit risky to travel during this time of year. Officially, the "hurricane" season is June through November but September and October are the most active months. As luck would have it, it's also the cheapest time of year to travel to Cuba so many people watch the weather reports and book last-minute deals!
3 - Dry, cooler, not as busy season (November through April). If 77-82 degrees (25-27 C) is what you are looking for with the best chance of not raining, this is the season for you. However, for many, this time of year is back to school, back to work, back to life -- so it's hard to take time off. But if you can, this is the best season to travel to Cuba.
Here are some graphs for visual learners (Celsius and millimeters graphs below too!):