How API integration works with other system

Hi All,
I have used MW almost 2 years and still don't get how does this API works. Most of our customer asking us about how to integrate MW with their CRM, Wordpress, RDBMS, etc...
My question are,
What will happen after integrate using API?
Is it means 2 system becomes one?
Is it mean they can login from their system and can access MW?
Every features in MW can be done from their system?