"Remain" probably represents sitting on the throne as king. AT: "Yahweh sits on his throne forever" or "Yahweh rules forever" (See: [[rc://en/ta/man/translate/figs-metonymy]])
The phrase "his throne" represents God's rule. Possible meanings are 1) "He rules in order to judge people" or "He rules over people justly" (See: [[rc://en/ta/man/translate/figs-metonymy]])
These two clauses express the same meaning. (See: [[rc://en/ta/man/translate/figs-parallelism]])
# He will judge the world with righteousness
Here "the world" refers to all the people in the world. AT: "He will judge all the people of the world righteously" (See: [[rc://en/ta/man/translate/figs-metonymy]])