Ecosystems in terms of tech are the services which a company (i.e. Apple or Microsoft) offer to make its tech work nicely together. Apple has iCloud and Microsoft has the Microsoft Account & Office 365, and let's not forget Linux flavour "Ubuntu" with its own online service.
It goes without saying that its in that company's interest to promote brand loyalty through its ecosystem but it pays to commit. As you can see from the diagram below Apple, Microsoft & Google have worked very hard to build their own respective ecosystems.
It could be said that trying to get one piece of tech to work with another alternative brand can feel a little like trying to put a square peg in a round hole, BUT when that tech is designed to work together life becomes much simpler! With the right eco system you can start thinking in terms of cloud-centric as opposed to computer-centric, for example when an email comes in multiple devices ping all at the same time and you just go for the closest device... Simples!
See also my post on Cloud Computing