IDK about clasping hands, as I don't do it. I do know that we bow our head in respect for the one we are praying to, God.
It is much the same in a legal case. When you approach a judge you address him differently than say a sales clerk. When you talk to the judge, your speech is more respectful as is your body language. When you talk casually to someone your mannerism change completely.
When we do these things for God, we are showing regard for his position of authority. We are also showing that we are in subjection to our father.
The clasping of hands may be to show love and encouragement for your brothers in the congregation. Hebrews 10:24-25:
"24 And let us consider one another so as to incite to love and fine works, 25 not forsaking our meeting together, as some have the custom, but encouraging one another, and all the more so as you see the day drawing near".