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I have an Android applications that assists users with finding the right credit cards to achieve their travel goals (e.g. sign up for this card and it'll get you 40% of the points needed to travel to Sweden in summer). Anyway, it's currently published as Tralue on the Google Play store (accessible via tralue.com as well). I'm in the midst of a major visual update that's sorely needed and am switching to the Holo (dark) theme.
The application icon shows up in the device's "all applications" list/launcher. The application logo is what will show up on the Google Play store page for my application. These do not need to be the same, but they can be. If they're the same, the icon should scale well, and I mean more than using Illustrator (e.g. add details to the larger version).
Examples of competing apps that you might look to for inspiration:
I don't know the first thing about design or marketing, so I'm very open to ideas about what the logo should look like. My only thought is that it should be travel-related, as that's the product I'm trying to entice customers with.
For specific requirements:
Logo: 512x512 pixels - PNG format, alpha allowed
Icon: minimum 48x48 pixels, scaling at the following ratios 2:3:4:6:8 - PNG format, alpha allowed
Further information on Android icons can be found here: http://developer.android.com/design/style/iconography.html
When you apply, send a link to your portfolio, and what your thoughts are for this icon/logo. Let me know if you have any questions. Thank you and have a great day!