The first time I heard the term microservice was from Andrew Noble the creator of Accziom where he offers microservices.
As pointed out by Dave McComb in Software Wasteland, there is a problem that causes software to be 10 times or even 100 times more complicated than it needs to be. Not having data centric applications (i.e. application centric or document centric) makes it harder to build software. I would take this even one step further and thinking information centric software.
Here is an excellent video, A Netfiix Guide to Microservices. The video has a nice graphic that I find useful in visualizing microservices.
Now, that video above talks about very low-level processes and tasks. Now, the notion of microservices can also be used to describe the tasks and processes involved in the full record to report process.
This graphic below shows many of those tasks and processes:
(Click image for larger view)
So imagine a "general ledger" microservice that can talk to a "transaction entry" microservice or a "close the books" microservice and so forth. Imagine that these microservices are intelligent software agents that exchanged standards-based inputs and outputs. Imagine that they worked at the "information block" level, effectively changing hypercubes of information held together by machine-readable accounting logic, the rules of math, and machine-readable accounting standards.
Today, there are plenty of these sorts of microservices that are carried out by an accountant, a report, green eye shades, and an Excel spreadsheet. Then tens if not hundreds of Excel spreadsheets are emailed around. Software silos are "integrated" using Excel spreadsheets, copying and pasting, RPA (robotic process automation), and other band aids and bailing wire to hook the kludge that people call their accounting information system together.
Break down silos rather than create them.