Rumblebuffin was a member of the Buffin giant family: one of the most respected of all the giant families in the Kingdom of Narnia, as mentioned by Mr. Tumnus. His character reflects that with him being of an agreeably gentlemanly nature while still a fierce ally in battle.
Rumblebuffin was turned to stone by the White Witch, but was eventually restored to life by Aslan (with Rumblebuffin stating that he must've fallen asleep) during the ransacking of the Witch's fortress.
After being asked his name by Aslan, and being asked to let everyone out, he used his club to open the door for Aslan and the freed creatures.
Rumblebuffin was featured in the BBC version, portrayed by Ken Kitson. His part in that version was the same, except that he kicks the door open. Upon the reinforcements arriving at the scene of the battle, Rumblebuffin swatted away some of the animated flying creatures.
Behind the Scenes
During in the video game of The Lion, the Witch, and the Wardrorbe, Rumblebuffin's design was seen as one of the bad giants in the White Witch's army where it marches with two unnamed giants in the First Battle of Beruna.