You can easily set up a web server on the ESP8266 and then have the Android app request data from that server: just send a POST or GET request to the ESP and have its server handle the request, then send back the data, e.g. as JSON string in the body of the http response. This is pretty straightforward to set up, but note that you're not sending data from the ESP to the Android app, but it's the Android app requesting data from the ESP. A little Google should get you all the tutorials you need on how to set up the two sides.
If you really need the ESP to send data to the Android side, you'd have to open some kind of service on the Android that listens to incoming requests, then have the ESP send requests to that service. I've never tried doing it that way around, can't even suggest specific protocols. You'll have to do your own homework there.