So I've increased the resolution of my image. Yet it is still showing grains in some areas. In the picture you can see that there are parts where this white grains suddenly flood up certain areas. I can't get rid of them. What could be some possible solutions?
Changing the resolution of the image merely renders it bigger. In the image below, I've change it to 500%, and that would blow up both the X and Y dimensions five fold, i.e. making it 6400x3600 pixels rather than the 1280x720 entered in the X and Y boxes.
From your screenshot, I'm guessing that you're using Cycles, and grain/noise in Cycles usually means too few samples. Try increasing the Render value under samples. What you need exactly depends highly on your lighting and materials among other things, so I can't say specificly what you'll need.
Changing the Clamp values usually reduces noise as well, by clamping out very high intensities.
You can read more about it here.