yes, some visual drawing or photo, in which a non-technical person would understand what your service is for. bitcoin.org is a good example.
They have a youtube video and some short explanation.
Inside an office money usually comes from a financial section to which the word 'api' is magic speak. Of course hackers like us understand it.
Your target audience is bussines, i assume?
As to why you would use it, it is managed, scalable, secure api. It is meant to make it easy to get data from the bitcoin network without hosting your own bitcoind, or having requirements. You run this from any server or application.
You want these words on your website in bold:
managed, scalable, secure