PrestaShop enables merchants to give third-party tools access to their shop's database through a CRUD API, otherwise called a web service.
About CRUD & REST
The PrestaShop web service uses the REST architecture in order to be available on as many platforms as possible, since the HTTP protocol and XML files are understood by most platforms, if not all.
CRUD is an acronym that stands for "Create, Read, Update, and Delete". These are the four basic operations for managing data in an application.
REST defines roughly a style of software architecture, which promotes the use of HTTP methods when building web application, instead of custom methods or protocols such as SOAP or WSDL. It defines several rules, including one that is similar to CRUD, which is described below.
HTTP has several methods that can perform processing on data as defined in the REST architecture, among which are 4 main methods. See this page: http://en.wikipedia.org/wiki/HTTP#Request_methods
The table below offers a comparison with CRUD and SQL:
HTTP / REST
Learning how to use the web service
The quickest way to learn the intricacies of the PrestaShop web service is to use the web service one-page documentation.
The slowest by but most complete way to learn about the web service is to follow the tutorial.