It's a good question, worthy in fact of a much greater and more in depth response than that which I'll be offering today.
In the most simple terms, different things, from salt, to sea shells, to gold, have all served the purpose of being currency at some point, somewhere. Cash is essentially a balance and ledger system in which we demonstrate what is owed to us by showing the value of the notes that we hold. Unfortunately that system is wide open to abuse, though again, that's beyond the scope of this post today.
What digital cash like Bitcoin does for us is provide a system which combines a unit of account with a value transfer mechanism giving us something utterly unique. One of the founding pieces of our modern banking system was created by the Templar Knights. Already involved with safeguarding the valuables of crusading nobility, they began to allow people to deposit their goods at a templar house in their home country, for which they would issue a note of credit, and the travelling pilgrim could make their way east without the risk of carrying too many valuables. As and when they needed to the traveller could withdraw an equivilent amount of wealth from various cities as they moved from city to city.
This caught on and even after the influence of the Templar knights waned, their practices didn't. Imagine how much safer it was to travl when you had no need to worry about your gold being stolen as you went about your pilgrimage.
Well, in the age of Bitcoin, suddenly that part of the banking system is now irrelevent. I can store wealth as a series of words or characters in my brain, I can enter those words into a mobile wallet when I get to my destination and then, once I've spent what I want, I can delete it again, safe in the knowledge that the only key to the funds was locked in my mind. If I don't tell anyone then noone can even know that I have access to that money. In short, the need for banks as trusted third parties that allowed us to transfer value over distance is no longer there. Cutting out the middle man cuts costs and anyone who has travelled or sent mony abroad can tell you that it isn't cheap or easy to send money around the world under the current system, even though it works.
There are other benefits, of course, such as the inability of governments to tax their citizens through inflation of the money supply when using Bitcoin, or the ability to program your money to only move under specific circumstances, a benefit which is being widly experimented with now in the form of smart contracts which only release funds when particular conditions are met. Imagine your children only gaining access to their pocket money when the teacher sends a form telling you that their grades hit a certain level, and then the wallet locking again if their attendence or grades slipped! Or your local mechanic only having the funds released to him once the cars on board diagnostics reports, via the Internet of Things, that the issue has been resolved. You could even have your tax automatically split and sent to each relevent party, directly (hospitals, police, roads, schools) without the need for a huge beaurocracy to oversee the collection and dstribution of those funds. The possibilities are both astounding and exciting.
Given we've moved into an age of abstract money which isn't backed by anything other than the issuing authorities ability to extract it from its productive citizens, this shouldn't be too tough for people to get their heads around once they start seeing concrete examples. That'll be part of the job going forward for people in our industry: showing people that there is a better way to do things. Once people can see there is a better way, with luck, they'll begin to make use of the tools which are being created for them.