Android malware isn't as big of a concern as some mainstream media reports would have you believe, but it is enough of an issue that Google started beefing up its security a few years ago. There's the "Bouncer" server-side scanning that checks apps before they go live, and your device runs app verification as new packages are installed. Now Google is about to patch a hole in the local app scanning by making it run continuously.
This change in app verification is going to hit virtually all Android devices by way of a Play Services update in the near future. The current behavior is to scan new apps and compare them to known examples of malicious code. If something is amiss, Android will alert you. After the Play Services update your device will do the same thing, but all the time.
The reason for scanning apps after they are installed is twofold. First, an app might be carrying a type of malware that isn't known when you install it, but is identified later. A seemingly innocuous app could also download malicious code through some external mechanism. Having app verification running in the background solves those issues. You might not even notice anything different, but you'll technically be safer.