Hi,
When WordPress installs a plugin, all it is doing is downloading a zip file, unzipping it, and copying the unzipped files into the right places. If this fails, it's almost certainly because your web hosting account disk space has reached 100% full. Around 20Mb is needed for UpdraftPlus - so, check that out, and you'll probably find you need to increase your account disk space a bit.
Best wishes,
David