Level 1 - the village
We start the story off where Jack just traded his cow or whatever for five magic beans. Now, Jack has to make his way back to his house without running into a troll who wants to steal his magic beans. If the troll touches you, you lose a bean. In this level, if you lose all five beans, the game ends.
Level 2 - up the beanstalk
This would play more like level 1-1 of SMB2, the part with the vines (if you don't take the shortcut). Jack climbs his way up the beanstalk avoiding the deadly bird. From levels 2-4, the beans will be replaced with lives.
Level 3 - the giant's castle
Jack must avoid the castle guard dogs whilst navigating the huge castle and find the magic harp and the goose that lays the golden eggs.
Level 4 - down the beanstalk
Jack climbs down the beanstalk avoiding the same deadly bird, and brings the goose and harp and Jack and his mother live happily ever after.