'Application Not Installed' is the general failure notice from the package manager in Android. it often means the app simply failed to install due to not meeting certain requirements (lib dependencies, storage requirements, Android version compatibility, amount of RAM, etc). only a logcat can decipher the cause, as Google is not too fond of giving the user the error details, and just gives a more dumbed-down failure notice.
Other messages include:
"There was an error parsing the package"
Which often means corrupt download, unfinished download followed by an attempt to install anyway, but can also be an app designed for a different version of Android which is attempting to be installed on a non-compatible version (such as an app requiring Android 4.1+ being installed on Android version 2.3 or lower). this one pops up outright, and does not say 'installing' first like the 'App Not Installed' error does.
"Insufficient Storage. Application Not Installed"
Often seen in Play Store but also seen on a sideload, this is obvious. the app refuses to install due to a space constraint, often accompanied by an icon in the notification area saying 'Low Disk Space-Internal Storage is low'. it can also be the result of a smaller system partition (not enough files the app needs can fit there) or a full cache partition (which will cause this error on larger apps, and one reason why Google made the 'additional file' download separate in Play Store.
"Package File is Invalid"
Despite the name of the error, this is not the real cause. a lot of times this happens on updates in the Play Store and it also produces an error dialog with the same message. often on larger apps over 20MB+. Usually means full cache partition or whatever the installer is trying to use for temporary storage to extract the file prior to installing. it runs out and produces this message. this one also happens after the 'installing' phase.