Possible answer #1:
The many times we bow during Shemoneh Esrei every day helps strengthen our humility before G-d, for bowing, according to a number of sources, signifies our humility and meekness before G-d.
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Possible answer # 2:
We bow when we say ברוך to show that even when we are feeling low, depressed and sad we still have to Bless HaShem. So we move our body physically low down and say ברוך - this is to demonstrate that we bless HaShem for everything that happens to us even if what happened makes us feel sad.
And then we stand up after we say the name of HaShem to show that since I am davening to HaShem and feel close to Him this will give me strength to stand tall and face the situation that is making me upset.