Microservices are a way to architect an application, by dividing all features into independently functioning services rather than maintaining one monolithic platform.
This conveniently coincides with the way many modern APIs work, that offer individual so-called 'endpoints' for each aspect you want to call the API for.
For example, if your application is a newsletter software, than functions like 'adding new subscribers', 'checking how many subscribers you got this week' and 'checking which subscribers clicked on a given newsletter' could all be separate, dedicated microservices corresponding to their own endpoints within the same API.
Developing a whole application as a sum of many microservices has become very popular as it helps split work up between different teams and allows for easier, continuous deployment of incremental updates.
A microservice is very different from a microapp. While microservices are stricly server-side, microapps are a kind bundling of applications into a single UI.
This doesn't stop some companies however from using the terms interchangeably. For example, Wells Fargo has adopted a new way of packaging business cases into their own microapps which they refer to as 'microservices' counter to the technical definition above.