Assuming that the Mobile is connected to Wifi router and supports 3G/4G data communication scheme(s) as supported by the router,The microcontroller can upload the data,either by streaming it continuously or by sending it all in one go to the Wifi router through ethernet...and the router can send the data.Only thing..How would the user on the phone know,that the data to be recieved is valid..would there be request to accept data asked to the user,like it happens when we recieve files using bluetooth..??
Ethernet is just the hardware layer. You need to implement a TCP/IP stack on the micro-controller to communicate with other devices via ethernet.
You haven't specified which micro-controller you are using,for the PIC mcus the TCP/IP stack from Microchip may be used. This is available from their website.
After implementing the stack on the micro-controller, standard TCP/IP protocols lile FTP, HTTP, UDP etc. may be used.
UDP is quite easy to implement on the micro-controller, but is also connectionless, so maybe you could use TCP. If you need to transfer files etc. then FTP may be good choice.
This again depends on the kind of data needed to be transferred. A web page on the micro-controller can be accessed by your mobile device, then the relevant file downloaded.
If you find all this difficult then maybe you could buy a embedded TCP/IP stack module like the Ez Web Lynx.
http://www.ezweblynx.com/
The stack is embedded in the module, you just need to load the web pages and send the data to the module from the mcu via serial port. This maybe useful if you need to show a web page with buttons, LEDs etc. and connect these to external hardware.
For a mobile device I think the easiest way of transfer would be via bluetooth...
thanks