From the story of Jack and Beanstalk come the magic sprouting plants. Jack was give several beans in exchange for a cow, planted one of the beans and had a giant stalk shoot up over night. When he climbed this stalk, he discovered the Cloud Kingdom, inhabited by giants, at the top. The mischievous Jack stole several items from the giants and escaped, cutting down the stalk so that the pursuing giants could not catch him. 

Wolves

When Bigby Wolf begins constructing his plan on how to defeat the Adversary, he plants a beanstalk on the Farm as a way of getting to the Cloud Kingdom. Then, sending Cinderella as a liaison to establish diplomatic relationships with the giants, the plan is under way. Cinderella's mission was a success, and the giants of the Cloud Kingdom agree to help the invasion force by digging a hole through their dimension over the Homelands. 

Bigby set out next to hit the Adversary where it hurt worst: his ego. Parachuting in alone, Bigby made his way to Geppetto's cottage and detonated his sacred grove, the source of all of his Wooden Soldiers. Escaping up the emergency beanstalk he had planted, Bigby detonated the base of the stalk before he made it up to safety, killing the soldiers that had began to follow him up. 

With the invasion beginning, the Fables army start to transport troops up the beanstalk with the help of the D'jinn. Once there, they parachute down into the Homelands and begin to amass their force. 

Bigby gathered his forces in the Homelands around the last beanstalk---the emergency escape plan for all of the Fable troops. Unfortunately, a wandering enemy patrol came close enough to the beanstalk to see it and reported back to the Emperor. What followed was a desperate attempt to guard the beanstalk under the crushing weight of overwhelming odds. Things seemed to be working until a magic arrow took both Boy Blue and Bigby out of the fight--the Fables two best fighters. The battle concluded in one-on-one combat between Bigby and the Emperor, Boy Blue getting the final strike with the vorpal sword.

Prince Charming explains that the beanstalk, in its essence, it trans-dimensional--it begins with its roots in one world and, somewhere up the stalk, transitions into the world of the Cloud Kingdom as some sort of magical gateway. Also, each beanstalk has a built-in cloaking field of sorts that makes it invisible to every form of detection until the person is almost upon it. Bigby said that a plane could fly within 300 feet of a beanstalk and never realize that it's there.