Most wifi libraries have an example of a HTTP client and a HTTP server - it sounds like you want both.
Is your Arduino on the same local network as your web application server? If not, it is easier for your Arduino to get to your application server on the internet (i.e. HTTP client) as your router is setup to allow this by default. If your application server is on the internet and tries to access your Arduino (i.e. HTTP server), most routers are setup to stop this as it is a security hole. You would need to setup a port forward on your router to the Arduino, but you have now opened your Arduino up to the internet.
As to putting the data in MySQL, that means you are going to have to poll MySQL from the Arduino to see if there is any new data there. You may as well stick with HTTP and have the Arduino poll a web service and have one less moving part (MySQL).