Yes if you buy a TIVO you have to subscribe to TIVO’s service for it to work.
If your cable provider gave you a box, it may have the same capability as TIVO, just a clumbsier interface.
You can actually use a TiVo box sans subscription, but you have to manually program the times and channels to record, like a regular VCR. I have had TiVo for years now and I have no idea how I lived without it!