The joke was so good that the whole room burst out laughing.
Literal
Extremely good joke was [because-ので], whole-room burst-into-laughter.
洒落 (しゃれ) means 'joke, witticism, pun.' 満場爆笑した is a dramatic compound: 満場 ('the entire room') + 爆笑 ('burst of laughter'). うまい means 'skillful, good' — applied to the joke's quality.