Is it legal to use to download videos from YouTube?

Short answer: it's legal if you're using it for your personal needs (time-shifting) to view YouTube content offline when over-the-internet broadcasting is not available.

Long answer: according to decision of the Supreme Court of the United States on the case of Sony Corp. of America v. Universal City Studios (464 U.S. 417), from January 17, 1984: "...time shifting was a fair use, represented no substantial harm to the copyright holder..." is simply allowing users to watch YouTube content later (time-shifting) when Internet connection is not available. Our service is a DVR for YouTube, which can be compared to the case with Sony and Universal in 1984. If you have no Internet connection, it's totally fine to watch downloaded YouTube content.

What is illegal about YouTube?