Just to build on @dotMorten_esri's answer: In order to open and read shapefiles, you will need a Standard level deployment license or higher (see the table in the License level and capabilities page).
You can get a Standard license either through a license string as Morten mentioned (you'll need to purchase a Deployment License Pack from Esri or your local distributor if not in the US) or you can use an ArcGIS account of appropriate user type. See this page to learn more about which ArcGIS accounts enable which license levels (but to summarize Creator, Professional, or Professional Plus user types would grant you Standard or above).
Note: you don't need a license for development and testing (simply don't apply a license and all capabilities will be enabled) but you must license your app before deploying to production.
