First make sure there is more than enough room on your device to fit the downloads. If there isn't, it won't work.
If you are trying to download from say Google Play Store I would says restart the tablet (turn it off and back on) and then try again. Also if you are trying to do this using 'data', I would turn 'data' off and try it over WiFi.
Should you still have problems, then I would try downloading something else to see if it works fine. If the other downloads work, there is something wrong with the one you are trying to download.
Now if you are trying to download from somewhere else, then the problem could be the place and not your tablet.