especially when it comes to computer jargon like some prior posts mention.
The JPG file format is compressed, that is, it looks at all the 1s and 0s of the image data and creates "shortcuts" to keep the image looking as much as possible like the original while making the filesize smaller. This isn't so bad if it's done mildly, it will remove just a little bit of detail from areas of the image you wouldn't normally notice (like the gradient of color in the sky) and the picture will look the same. But if you do it too much, it will start removing detail from everywhere, and the image will look overly-pixelated.
Here's an example; This is an image where detail is critical, so I've saved the file as a JPG with the highest quality/as little compression as possible. The filesize on my hard drive is 504 kilobytes.
The image you see above is also 504 kilobytes, so my photo service is just displaying the file as-is, no changes or compression added. It looks as it should, I wouldn't want any compression to steal even the tiniest detail.
So now let's see a compressed example, let's say my photo service has decided that their drive space is precious, so they're going to add compression to files they deem too large. This is a somewhat exaggerated example, but it gives you the idea that compression means lost detail:
Ouch. The filesize of this image is 11 kilobytes, so while the file takes up a lot less space, it's also lost nearly all of its fine detail. If this were some sort of important one-of-a-kind photo, like a family portrait, all future generations would only have this pixelated idea-of-a-picture - this is what can happen when data is lost.
So what everyone is talking about here is how some of the various photo services are applying compression to the images; if you feel your photos are important, if you want everyone to see your pictures exactly as you see them, then you obviously want a service that doesn't tamper with the file/doesn't add compression.