I am not trying to give the usual definition of what is Big Data as there are umpteen definitions already.
Big data is a new wave [that has been used by many companies for so many years already:-) ] to make existing proceses and applications smarter :-)
It is like the smartphone revolution that we have already seen. Most applications have a smartphone interface because it makes the application smarter and improves user productivity.
Look at what Facebook kind of services itself did with your personal data. They suggest friends and bring in people you would not have thought of as friends. This is increasing the expectations of the business on application teams. It is driving companies to use their existing data and make their applications smarter, in the end help them make better business decisions.
Here is another example. Say you have moved in to a new city and are not familiar with the train timings. However your friend or a friend's friend, lives in the same city. She uses the "Train Station finder App" which she really likes. For you to know about the App, in the traditional way, would normally have been via newsletters or advertisements of the Train Station itself. But now, with the data that facebook kind of service has, they can now suggest that you use it since you just moved in to the same city. Now when an app marketplace suggests or advertises that to you, you are happy as you think that is relevant news for you.
And now with mobility there is a lot more data. Location. Social. Mobile. Tablet. Ways for an application to be human friendly. Lots more unstructured data that needs custom rules/queries applied. Incidentally that means, terabytes of data that need newer technologies to store and process for meaningful consumption.
In other words, Big Data is about making your applications give a wow effect to your user.