Does "u have my word" more formally than "i promise"

what's the "did time“ meaning in the lyric? "Yeah, my heart did time in Siberia Was waiting for the lie to come true 'Cause it's all so dark and mysterious When the one you want doesn't want you too" (bsb's lyric) what's the "did time“ meaning there? thanks.

First notebook entry: Introducing myself I wonder if the English name Alan is suit for me,my family name is Chong.I need suggestion,thanks.