What does it mean to reconcile an account?

It's to prove and/or document that the account balance shown in the internal files of the company is correct, using external data sources (like bank statements for example).

That way, you reconcile two versions of the reality to make sure you are telling the same story.

Once the account has been reconciled (usually by an external party), you can use it confidently in your decision making process or share it with other parties (like banks, governments, partners, and so on).