Pennie - yes this is called Cutwork. It is a type of embroidery and can most certainly be done by hand. But not me -ROTFL - I do it on a machine!
I have an embroidery machine so it is really very easy to do. Basically the machine stitches out an outline of the completed design; I then carefully cut away the fabric where there is to be 'gaps'. Once the fabric has been removed, its back to the machine and let it complete the design.
The hardest part, apart from the careful cutting, is laying out the design in the beginning. Taking the time to draw centre and placement lines means a neater more professional finish, although I have to admit I am still not perfect in my placement.
The design can be as simple as a few areas of cutaway fabric to something almost like lace.
A Supper Cloth - or an Afternoon tea cloth - is a small tablecloth; the idea was that for supper or afternoon tea a full table is not set so a small cloth is thrown on one end of the table and set with china and yummy cakes etc. You could also use it as a topper over a larger plain cloth or on a small round table.