Many different mobile phone operating systems have different application stores (app store for short) where you can download applications to your phone like Symbian which runs on high and middle end Nokia devices like the Nokia N8 which runs Symbian^3, Nokia 5230 powered by Symbian S60, and Nokia 5130 powered by Nokia Series 40 platform.
Platforms: Symbian S60, Symbian^3, Nokia Series 40, MS Windows Phone 7 (coming soon)
App Store Name: Ovi Store.
Major Makers: Samsung, LG, Motorola, Sony-Ericsson, HTC
App Store Name: Android Market.
Major Makers: RIM
Platforms: BlackBerry 5, 6, 7, QNX
App Store Name: Blackberry App World
Major Makers: Apple
App Store Name: Apple App Store
Address: iPhone App Store
I will still update this page with more details but you can visit the relevant website of the mobile platform that your phone runs on.