Earlier quoted context omitted.
Well, you can, if it's an image or a video.
... and is saved in the camera roll (not all images are there. for example a drawing app doesn't put its stupid images in your camera roll!)
This is really a lowest-common-denominator for file transmission - for example, until recently my mom couldn't upload her photo on meetup.com due to this limitation (she uses only an iPad)... I figure Apple cares more about her needs than mine (saving specs.xls into a JIRA).
Any other file uploads (docs, etc) are likely better handled by an app or simply email.