Tonight's moon will appear full again tonight and it will experience its closest contact with earth for the remainder of the year. When the moon happens to be full, and within 90% of its closest approach to Earth in its typical orbit, it's called a "Supermoon." This is forecasted to happen again next month, but tonight will be the closest of 2013. It will appear larger than what you're used to seeing a full moon look like.
This June supermoon is also called the "Strawberry" moon. According to the Old Farmer's Almanac, this is because "Algonquin tribes knew it as a signal to gather ripening fruit."
Whatever you call the moon, expect tonight's visibility to be fair for the most part. As showers die down this evening, the skies should clear up.