(note: I put ' before stressed letter below)

In these examples "сто'ит" is form of "сто'ять" verb (to stand). It's meaning in these cases is similar to "to reside / to exist / to stay (somewhere)". "To be" is close enough. Remember that in russian "to be" is omitted very often. It is the case. "У нас ясная погода." is ok. "У нас есть ясная погода" is not ok. It is unusual to have "to be" in such phrase. So, "стоит ясная погода" is common replacement if you want to omit "у нас" also.

Also there can be "ст'оит" derived from "ст'оить" (to have cost/price). It's really another verb and another meanings.