Parse is a sdk cloud for rapid application development. With it you can store data, send notifications, emails, track facilities and a lot more things the app needs.
You do not need to store your business data there; you can simply send Push notifications to your customers when you find it convenient right away of your system.
For push to work, you need to include the parse SDK in your mobile project and register the installation. The site has a step step , if you follow you will be able to do without any problem. I've already done it for android and iOS, it's really easy.
Regarding the limits the parse has some plans here . Personally I've always used it, and I use it today, and I've never paid anything, but it counts the amount of access to the API and can charge you if you send a lot of monthly requests, so that's up to you.
One thing you did not ask, but I'll tell you, is that parse has a major latency problem, so it's not very good at saving data that needs to be queried and loaded all the time. Use sparingly.