Try downloading a different app, any old app, just to see if it's something specific to the app you're trying to download or something else.

If you can download other apps then the following might help: go to settings, then to security, then to 'unknown sources' and toggle it to 'on'. It might help to let the app install. Make sure you turn it back off afterwards.

If you can't download any apps try logging out of your Google account and logging back in - and make sure you're logging in with your Google account and not another email account. It should be your Gmail log in details.

Did you check your storage to make sure there is enough room?