A trader may have multiple market watches depending on how he likes to categorize his scrips. It may be Nifty50 / midcap / smallcap, or by industry such as Auto / Pharma / FMCG, or by Futures / Options / Underlying, or by portfolio type. Group Settings help you manage multiple market watches (assume a MW is a group).
Remember that, in NOW, a MW can have a max of 55 scrips, though it is usually kept smaller so that all are visible on the screen. You will find that Group Settings is mostly used near expiry. Also, the groups are saved so that you see the same settings in the NOW terminal and the web based version.
To delete a scrip from a group / market watch, select it and press Del.
In your image, you have not yet created a group. Give a name and click Add Group; it will show in the Group Name list. The context menu, when you right-click on an item in this list, shows many powerful options.