list of all accounts of company for the period is called 
trail balance

First of all, it is spelled as 'Trial Balance' not 'Trail
Balance'

A trial balance is a statement of ledger account balances
within a Ledger, at a particular instance.

If we balance all the ledger accounts at a particular
instance and then prepare a statement of balances we get the
"Trial Balance". 

The purpose of preparing 'Trial Balance' is to check the
mathematical/arithmetic accuracy of accounting.

Mohsin Pervaze. Shm  Answer is absolutly correct as well as
sufficient.

Trail Balance is the summary of balancing figure of ledger 
of each transaction and it verify airthemetical accuracy of 
ledger.