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I have installed Linux Mint 18.3 Sylvia, when ever I open System Monitor, the process Cinnamon is taking so much of my memory and CPU. What is this cinnamon process and what is its significance.

The cinnamon process is the window manager that's drawing your screen. If it's causing you issues you can do the following to kill it and replace it with a new instance.

$ pkill -HUP -f "cinnamon --replace"

The cinnamon process is the window manager, i.e. the program which manages all the windows on your desktop. It also takes care of the desktop, the panel, notifications etc.

Cinnamon is your desktop environment. Essentially your GUI. It's what you see when you use your computer.

So, to answer your next question, no don't kill it! :) It is quite normal that it takes a lot of RAM. On most systems, the graphical environment is very RAM-hungry since our modern GUIs come with all sorts of fancy bells and whistles. Cinnamon isn't the most complicated and heavy, but it's far from the least.

On a final note, remember that used RAM isn't a bad thing. Unless you feel the machine is lagging or slow, there is absolutely no problem here. Most of the RAM you see used is probably marked as available to other programs and will be released as soon as anything asks for it. You can see this by running free -h:

$ free -h
 total used free shared buff/cache available
Mem: 31Gi 9.6Gi 16Gi 2.7Gi 5.6Gi 18Gi
Swap: 14Gi 3.9Gi 11Gi

I don't use Mint, so I don't have this "System Monitor" you mentioned, but I'm willing to bet that it's showing the buff/cache value as part of the "used".

Finally, to understand more about Linux and RAM, have a look at https://www.linuxatemyram.com/.