REST is REpresentational State Transfer. I consider it more useful than SOAP because SOAP uses only XML for transfer but REST uses both XML, JSON. (since I love JSON) and feel easy to handle JSON.
You should create an API for your application because you should build your application architecture such that only one part can access the databases (eg: Model) you should not allow view or controller to touch the DB (just saying for an example with MVC You can follow with any other custom architecture). So for Model to get data you need to build some API which gives data on request to it. (eg: you may want data in a table so you will write API to get data in that table and when your application will ask for data from this your api will provide the data for you).