In this blessing we ask HaShem 1. to restore His Presence in Yerushalayim. and 2. to reestablish the Throne of David. This double request alludes to the spiritual and the political aspects of Jerusalem.
First of all, Yerushalayim is the city of the Bet haMiqdash . The Bet haMiqdash was the Holy Temple. The soul of the Jewish people. We Jews believe in God's Omnipresence (=God is everywhere). However, the Tora asserts that in the Sanctuary there was a special "Divine Manifestation" (Shekhina), a feeling of God's presence which could not be experienced anywhere else. It is impossible to describe with words how this "God's Manifestation" was felt. However, if upon visiting the Western Wall (one of the outer walls of the Temple) you are overcome by an incomparable sensation of Holiness and closeness to HaShem, the feeling you experience in the Wall, is a tiny reflection of that overwhelming "Divine Manifestation" felt in the Bet HaMiqdash. In this Berakha we first request God to reestablish His Manifestation in Yerushalayim. Restoring His Sanctuary, the Bet HaMiqdash.
We also pray in this Berakha for the reestablishment of the "Throne of David". Aside from being the spiritual center of the Jewish people, Yerushalayim was also the political capital of the Jewish Nation. All National Institutions were established in Yerushalayim. In this aspect, Yerushalayim was to the Jewish Nation what Washington DC is to the USA. The Jewish King had his palace and residence (=the White House) in Yerushalayim. Yerushalayim was the residing place of the Bet Din haGadol (= the U.S. Supreme Court of Justice) and Yerushalayim was the city of the Sanhedrin (= the U.S. Congress). When we cry for the destruction of Jerusalem we lament not only the destruction of the Bet HaMiqdash, but also the eradication of all our political and governmental institutions. Thus, in our Berakha, when we pray to HaShem for the reestablishment of Yerushalayim, we also pray for the restoration of the Jewish Government (David's Throne).
Today, Baruch HaShem, we have Yerushalayim again. But we still don't have the Bet HaMiqdash. The Bet HaMiqdash is to Yerushalayim what the soul is to the body. Now, if Yerushalayim is today the most beautiful city in the world, and this is Yerushalayim without her soul, imagine how magnificent Yerushalayim will be, once her soul, the Bet HaMiqdash, is restored!