Reconciliation is the process of going to your source system, getting a number and validating that number on the target. This ranges from being easy to impossible, so you need to decide what to reconcile on a case by case basis.
In its simplest form, we can go to a source system and find out things like how many records are to be copied, sum up totals and run other aggregations that we can then validate as correct (or not!) on the target system.
Ed has put together a thoughtful approach to validating data loads regardless of the source.