So how are you trying to install these apps? Are those things download links for the apks, or links to some app store? What app are we looking at in your screenshots (the app you are running, not the ones you are trying to install).
If you are you downloading apks from some site and then trying to install them (i.e. not using the Play Store) you'll need to give one of your apps the permission to install apks on your phone. Look in your "Security and privacy" settings for "install unknown apps" (or just search settings for "install") and this will give you a list of apps that are capable of installing others. Tick the switch to give one of them the permission and see if that fixes it. Personally I prefer to give it to a file manager rather than a web browser: to me it always seems very insecure to let a browser install apps, since the browser is the app that is most likely to be exposed to malicious websites that might take advantage of this (whereas if the browser can't install apps the worst that can happen is that an ad or site can download an apk to the phone but can't install it).
If those links are doing something else, then please tell us what. Because that's the problem here: I can see that these are screenshots from your phone, but I don't know what app you are running and what exactly it is trying to do, just that it clearly isn't the Play Store.