When you have an account that is linked to your mortgage. The money in it is deducted from the principal of the loan each month, so you end up paying less interest each month. This then shortens the life of the loan and you can pay off your house sooner....!
Basically the bank is saying " hey! See this money you have saved up? Well you could use that to pay off a chunk of your loan!" To which you reply... " but I might need that money to buy groceries, or a Ferrari or stuff" and the bank says " well we'll pretend that you are going to use it for your loan but if do you need some money then you can withdraw it from the account anyway"
So with an offset account it encourages you to save like crazy because the more you have in there, the less interest you pay. If you save enough then you can match the principal or even exceed it at which point you are paying no interest at all and are only having the principal deducted from your repayments each month! Then at any point, you can pay off the loan in a lump sum if you wish or keep that money for a rainy day event.
On my first house we did this. Saved up more than the outstanding principal to the point where we were $20 000 up. Then went and paid off the loan in a lump sum of about $50 000. I also paid all bills, cleared the credit card etc etc and so were absolutely debt free... For 24 hours, because the next day we went and bought our investment house/rental and borrowed off the bank again... However we've since done the same offset thing with that house, borrowed on the equity increase value of that house, sold our previous house, and that's why I currently own the house I'm in now...! (Outright)
If we ever get into financial difficulties we can sell the investment house, pay off that loan and still get to pocket the equity capital gains (profit on the increase in value over time) ...less taxes of course (which in Australia is 50% of that capital gain...Dammit) The investment house has doubled in value since we bought it btw...
My wife is one smart financial whizz... :+)