Q. If there is no eruv, why is carrying things not allowed on Shabbat? Why does an eruv make it better?
A. The Biblical rule is, “Bear no burden on the Sabbath day” (Jer. 17:21-22). The halachah distinguishes between a burden and an adornment. Carrying a burden, however small, from place to place is not permitted on Shabbat, but wearing an adornment such as a ring is. The concept behind not bearing a burden is that weekday activity, eg buying and selling, involves moving things from place to place.
On Shabbat we have symbolically a closed society in which we withdraw from outside activity. Even with an eruv we still have a closed society except that its boundaries have been extended. Things we need for the observance of Shabbat such as siddurim, reading glasses, etc., may be carried inside the eruv, but things which are intrinsically inappropriate on Shabbat such as money, pens, etc., remain muktzeh and may not be carried.