During prayer now-a-days why do people bow their heads and lean on their arms? What’s the purpose of this and how did it originate?

This is done during a service called “Tachanun” – literally “Supplication”. It seems that bowing in prayer as a symbol of submission is found across almost all cultures and religions. However, according to the Torah, complete prostration is only permitted in the Holy Temple. Without a Temple, the Sages instituted a different sort of bowing which would not transgress this prohibition. Originally, the practice was to bow on bended knees with the head to one side (perhaps resting on the arm) as opposed to directly on the ground. This eventually evolved into the practice we are accustomed to today.