Actually, that's not a bad explanation. Any trial balance is just the balances that are currently in all of the accounts. When it's specifically refered to as unadjusted, it's prior to making any period-end adjustments. It doesn't really matter what exactly those adjustments are -- whether it be insurance or whatever. As long as no adjustments have been made, then it's an unadjusted trial balance.
As opposed to an adjusted trial balance, which is after any adjusting entries have been made, to reflect those new entries.
The adjusting entries themselves is a subject needing addressed separately since it can involve many different types of entries.