For questions concerning the 'Allow unknown sources' setting (which must be enabled if you want to install apps from sources other than Play Store). If your issue is about the installation itself, use the 'side-loading' tag instead.
What is the "Unknown Sources" setting?
Its location in Settings→Security already makes clear it is a security related thing. If disabled (which is the default on most devices), the only source you can install apps from is the google-play-store. Only after enabling it, you permit apps from other sources to be installed -- a process known as side-loading.
What are the risks involved activating this setting?
Permitting apps from "other sources" to be installed on your device might introduce the risk of drive-by downloads -- at the most if you tend to simply click "OK" whenever a popup window asks you something (as you still must approve the side-loaded app's permissions). Actively installing apps from unknown sources might introduce the risk of malware as well, if those sources are "untrustable" or even just "unknown".
Why should I enable this setting then?
There are still good reasons to use this feature. After all, on each installation you have to acknowledge the permissions of the app-to-be-installed, even if those are trivial or non-existing. Good reasons are e.g. if you have trouble with some app, and the developer sends you a fixed version to test (at least, if you can trust him). It is also required to use 3rd party markets such as e.g. AndroidPIT or Amazon.
