You need to export the image into a format that can be used on web pages.
You have 3 choices: JPG, PNG, or GIF - these are the only formats supported in all web browsers. For photographic images on the web JPG (jpeg) offers the best compression to quality ratio, and the smallest file sizes. PNG and GIF are for web graphics.
To export in GIMP hit File > Export > give your file a new name and end with the extension .jpg, hit Export, when the export dialog appears, set the quality slider to maximum (for the least compression). The lower you set the quality, the more compression is added, but the worse the quality gets - so max out the quality if you want as little degradation as possible.
A word of warning: before you do that you should also save your edited image as an XCF - in GIMPs native image format, you will need that if you ever want to re-edit. XCF saves images with layers, text layers, and layer masks intact. None of the other formats save that kind of stuff, because these file formats don't support it. Also XCF is a lossless format, it is uncompressed, therefore the quality is never compromised.
When uploading to external websites such as twitter, sometimes these social networking sites strip any metadata (the EXIF data), this may be outside your control. Facebook does this too.
If you get a free flickr account at flickr.com and upload the images there - that service doesn't strip metadata - if you want to upload the full resolution images to flickr you need a pro-account. Other alternatives you could use are dropbox.com which gives you 2GB of free storage - full size images are allowed, and no striping of EXIF/metadata either.