iPhone devices started the smartphone craze which would go on to replace conventional mobile phones in both Japan (which had its own subset of cell phones) and the rest of the world, with more advanced touch-controlled devices.
Unlike their direct competitor, Android-based smartphones, they have currently no working emulators, as the official iOS SDK (Mac-only) only allows for running your own projects, i.e. they run code generated for an x86 target rather than ARM code as used by iOS.
Many of the currently available "simulators" only try recreating popular iOS apps (like browsers) in a PC application with no real emulation involved. Some notable scams in such fashion are called iPadian or variations on the name, and are often adwares. A project to emulate various smartphones (iPhone, iPod Touch, iPad, Apple TV 2G) called iEmu, started in 2011 but got mysteriously abandoned two years later before anything usable surfaced. There has been recently a project to convert iOS apps to Android apps but nothing released yet as well.
Your best bet, until a new emulation effort is ever started, is to hope for whatever iOS app you are interested in, to have an Android port. Which is often sadly not the case (until very recently) for the vast majority of the older game apps, especially Japanese ones - as the Android is perceived often to be the more piracy-friendly platform. That appears to be gradually changing lately, and isn't as much concern for non-gaming apps, but the older apps are unlikely to get ported for the most part.
iOS apps are distributed in the ipa format. Like its Android counterpart, apk files, they can be opened as a regular zip file most of the time and their contents dissected this way.