Most people treat their smartphones like they treat their computer. It looks good on the outside but internally it’s crap. The phone lags, some apps eat up your battery etc.
Here are a few apps to help diagnose some issues your Android device:

SeePU (free): It will show you the current CPU, RAM and data network being used in the notification area. I always use just the CPU & RAM.

SystemPanel App/Task Manager(paid): You can try out the free version first which also show you current RAM, CPU, Storage values and gives you the ability to close apps like a task killer would. The advantage of the paid version is it will give you the ability to consistently monitor your phone and give you detailed information on each app’s CPU usage to help you find out what’s eating at your battery.

Watchdog Task Manager(paid): There is also free version for this app which should be fine for most users. This app will basically give you notifications when specific apps are misbehaving by using too may resources(CPU) on your phone and give you the option to kill that app. You can white list certain apps to stop receiving notifications. The paid version will give you the ability to blacklist specific apps that are constantly misbehaving and set cpu limits that if reached will automatically kill the app.

P.S.: Auto task killers are not good for your phone if you’re blindly killing apps. Unlike Windows for PCs, Android OS was built to handle memory efficiently on its own. Unfortunately, poorly coded apps can negate that and affect your phone adversely.