The reason for that warning message is that, if you install Office and don't activate it, it will largely stop working after 30 days. You'll still be able to open & read files, but you won't be able to create, edit or (possibly) print them. If you don't save the product key somewhere, you'll have difficult re-installing Office at a later date if, for example, you need to wipe your system and start over again.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]