The last of the 39 melachot (creative works prohibited on Shabbat) is that of carrying between a private and a public space. How is carrying a creative work?
The 39 melachot are all based on the activities that were needed to build the Tabernacle in the wilderness. Carrying objects from place to place was one such activity. Carrying a heavy wooden beam certainly is laborious, but equally prohibited is carrying a book from one house to the next, which might not feel like labor at all.
The Biblical prohibition of carrying is only from a private domain into a public domain (and vice versa) or carrying 4 cubits in a public domain (about 6 feet). Within a private house, a person may carry objects in any part of the house. In fact, as long as one’s property is completely fenced, one may also carry things outdoors (within the fence) because the fence firmly proclaims the extent and boundaries of private property.
What one may not do is to carry an object from a private domain into the public domain - the sidewalk, an unfenced yard, etc - even if one’s goal is to bring the object to another private domain.
This law applies to all things. And carrying does not only mean having something in one’s hands, but also in one’s pockets or over one’s shoulders, as well as pushing an object (such as a stroller).
Why then, do we see so many people wheeling small children and carrying diaper bags on Shabbat? Those who live within an eiruv, a rabbinically constructed boundary that creates a private domain out of a large public area, do not have to worry about the prohibition of carrying. What the specifications of an eiruv are and how it is created -- will have to wait for a future Treat.