WOW! That is "drawn thread work" or "drawn thread embroidery". Because it's all in white, it's also "whitework".

Individual threads are cut and pulled out, leaving patches of the original cloth, with areas of crossed or parallel threads, and embroidery stitches are worked over the remaining threads. And sometimes freestanding "needle lace" stitches were used. It's a complex work.

Hard to tell where it is from, because it was done all over the world.

You can repair the hole by carefully re-weaving a matching thread (probably linen) into the pattern and embroidering over it.

Actually, I don't think it's drawn thread embroidery. What looks like the cloth has little uneven dots, which looks like it would be a bobbin cloth stitch, especially if you look at my second picture, pictures,can see what I mean.

Looks more like this stitch here, I think

It is handmade bobbin lace. I had a co-worker who collected it. I bought a number of pieces from her when she culled her massive collection.

My mother did drawn thread work, this is not it.

Your piece is extremely fine work...much better than commonly seen. For the repair I would suggest carefully mending with some fine crochet cotton, where you could match the color. Mine are all cotton, not linen. I can't tell with yours without feeling it, but odds are it is cotton.

I bow to the masters ... I didn't realize that bobbin lace could imitate cloth like that.

Any idea whether it's valuable? Right now, it has yellowed in some areas. How would I wash it without ruining it?

It may well be - however, be warned that this is a hard time to be trying to get good value if you're a private person looking to sell.

it's damned fine work (the layers on the flower petals boggle me) and slightly yellowing is acceptable in older pieces.

you can wash it, gently, by laying it in the tub with warm water and a tiny bit of shampoo or detergent for delicate fabrics, and letting it soak for about 10 minutes.

oddly enough, the best whitener? is sunlight an chlorophyll, so if you have a CLEAN lawn, or a nice soft bush to drape it over, that's not a bad way to dry it.

this one, by the way, looks as if it's been very lightly used - the thread has not 'fuzzed' at all from being washed, and it looks like it still may have sizing in it (they were often starched after drying)

Thanks for all your feedback.
I wasn't really trying to sell it --- although I have to admit that I'm not sure what to do with it and probably don't appreciate it as someone else might. I was more concerned that I was going to ruin it up by trying to wash it, and even more so by trying to fix the slight tears and the bigger hole in the middle.

My other question is: Do we know it's a table cloth or could it also be a bed spread?

I have two of them.One was from my MIL's family. The other was in a batch of tablecloths that came with a vintage table I bought on CL. I love both of them!
I have washed both of them on the handwash cycle of my washer and hang dry. I would repair the holes before you wash them.They are definitely tablecloths.
I think there was a post on here about a similar tablecloth Flyleft was the OP. You might search for her name in this forum to find it.

Thanks, Cooperbailey. I looked up the post initiated by flyleft.However, her tablecloth is obviously in a completely different league.
What do you think my tablecloth may be worth?

A similar bobbin lace cloth was on First Dibs for an asking price of a couple thousand.

It's a matter of getting it properly repaired, cleaned, and in front of the right buyer.

Yeah, well, I also had a china cabinet that was for sale on 1st Dibbs for 12K, which I sold on Ebay for 1K.

Where would I go to get it properly repaired since I'm obviously not qualified for that?

I believe this was discussed previously on this board, and this type of "lace" is called Cluny.

I think you are right. Definitely looks like my table cloth. Have been reading up on Cluny bobbin lace, and fortunately, it doesn't sound like my table cloth is worth thousands, so I can go ahead and use it.