“The latter glory of this house.” The context indicates that this “latter glory” will occur in the Millennial Kingdom and refers to the Millennial Temple described in Ezekiel 40-47. Because of the sin of the leaders and people, the glory left the Temple and Jerusalem (cp. Ezek. 11:23 and commentary on Ezek. 11:23). It will not return until the Millennial Temple described in Ezekiel 40-47 (cp. Ezek. 43:2-5; 44:4). [For more on the Millenial Kingdom, Christ’s 1,000-year reign on earth, see Appendix 3, “Christ’s Future Kingdom on Earth”].
“this house.” The Temple was referred to as “the house,” i.e., the house of God.
“The former.” The former “house” was Solomon’s temple.
“prosperity.” The standard rendering of the Hebrew word shalom is “peace,” but it means much more than that; it means peace, wellbeing, wholeness, prosperity. Especially in a context like this, “peace” is too limited. God is promising that in the future Jerusalem there will be shalom, prosperity, wellbeing. Of course this could only happen in a time of peace, so peace is certainly included. There are many prophecies of the prosperity and well-being in the future earthly kingdom of Christ. The NRSV and Rotherham's Emphasized Bible also say “prosperity.”