Shemoneh Esrei is divided into three parts: praises, requests, and thanksgiving. In reciting the first three berachot, we resemble slaves who offer words of praise before their master. While reciting the middle blessings we are similar to slaves who make requests of their master. When we recite the last three blessings, we are like slaves who gracefully accept reward from their master, then are dismissed and go on their way (Berachot 34a).
We learned this from the prayer of Moshe Rabbeinu, who opened with praise and from there continued to plead and request (Berachot 32a; also see the laws of Pesukei d’Zimrah in this book 14:1). Without the introduction of praise, there is concern that our prayer will resemble the rituals of idol worshipers, whose entire aim is to mystically manipulate the higher powers to work for their benefit. In contrast to them, we want to serve Hashem and devote ourselves to Him, and all we ask is that He bestows abundant goodness and blessing upon us so that we can reveal His Name in the world. Therefore, first, it is incumbent upon us to know before Whom we are standing in prayer. We stand before God, the great, the mighty, and the awesome, the One Who sustains life and resurrects the dead, HaKadosh Baruch Hu. With that understanding, we can approach Him and pray with a pure heart for all of Israel and for ourselves.
Indeed, in the section of the requests, in which there are thirteen berachot, the general ambitions of the nation of Israel are expressed. They are not intended for the individual advancement of the person praying; rather the essence of the requests is about revealing Hashem’s glory in the world. Even our personal requests for health and livelihood are to allow us to participate in the rectification of the world (tikun olam). The following are the thirteen themes for which we ask: wisdom, repentance, forgiveness, redemption, health, livelihood, the ingathering of the Jews from the exiles (kibbutz galuyot), the return of justice, the destruction of those who hate us, the blessing for the righteous, the rebuilding of Jerusalem, the re-establishment of the kingship of the house of David, and finally, that our prayers be heard.
After the requests, we end the Amidah with three general berachot, in the center of which is a thanksgiving blessing concerning our lives and all the goodness that Hashem constantly bestows upon us. Before this, we pray for the return of the Temple services, and after it, we recite a berachah for shalom, since shalom is the vessel that encapsulates and sustains all the berachot.
Here is the place to note that the Shemoneh Esrei (which means eighteen) is actually comprised of nineteen berachot. At first, when Anshei Knesset HaGedolah instituted the Amidah, it was made up of eighteen berachot. After the number of slanderers and informers increased, following the rise of Christianity, which preached the hatred of the Jews, the Chachamim instituted an additional berachah for the saving of the nation from the hands of the apostates and slanderers.