what is intel x86 atom system image in android sdk manager?

So my question is, what is intel x86 atom system image in android sdk manager?

It is a version of the Android emulator that runs natively on x86 CPUs, like those in most development machines.

Contrast that with the ARM system image, which contains ARM (not x86) CPU instructions, and therefore must be translated when run.

Should i install it or not?

The x86 emulator images, where available, tend to run faster. You will have to do some work on your development machine to take advantage of them, as is outlined in the documentation.

the option is present in api level 15 & 16 but not in 17.

AFAIK Google relies upon Intel to create these images, and Intel has only done so on a few API levels.

The x86 Android* emulator system image enables you to run an emulation of Android on your development machine. In combination with the Android SDK, you can test your Android applications on a virtual Android device based on Intel Architecture

Whether I should install this?

Yes, if you are using Intel processor. To check if your intel processor support Virtualization Technology(VT), use Intel Processor Identification Utility tool.

Note: If your CPU does not support virtualization technology(VT), then you cannot use virtual machine acceleration.

In order to install the emulator image add-on, you can use the Android SDK Manager (Recommended Method):

Install Guide(Recommended Method)

Alternately, you can download the binary zip file and unzip and copy the included directory into the add-ons directory of your Android SDK installation. (Note that this method does not allow for automatic updates of the add-on):

Install Guide(Alternate/Manual Method)

Hope this helps.