You're allowed to leave the house on Shabbat! The eruv (string around the neighborhood) is to get around the prohibition on carrying things between a "public"

You're allowed to leave the house on Shabbat! The eruv (string around the neighborhood) is to get around the prohibition on carrying things between a "public" domain and a "private" domain. This prohibition is very broad - having your house keys in your pants pocket as you leave your house counts as "carrying" as does pushing a stroller. The eruv allows the whole neighborhood to be considered a "private" area and sidesteps this prohibition. However there are definitely Jewish communities that don't have an eruv or wouldn't make use of it if there is one in the neighborhood.