TiVo is a commercially available PVR unit. It's credited with being a major influence on MythTV (but not in a patentable manner of course!). TiVo ushered in the idea of a DVR, and included a host of useful features like 30-second skip, (which has been removed by default but is still available via a special code). As DVRs in general have become more popular, broadcasters have placed more pressure on companies like TiVo to provide features that benefit broadcasters instead of customers. TiVo has done a respectable job of trying to walk the fine line of keeping both broadcasters and customers happy.
TiVo has a reserved hard drive area that can be used to store commercials and other promotional information that the TiVo interface displays to a user in a non-intrusive way (it does not force you to watch advertising before allowing you to perform any action). A TiVo unit can collect general data about viewing habits, and also offers users the option of providing more specific data collection on an opt-in basis.
Units similar to TiVo have become available on the market, but none have gained the wide market acceptance of TiVo. Often these devices can be purchased at a cheaper price than a TiVo unit, and offer similar functionality.
Artful users have been able to modify TiVo units by adding larger hard drives, a process that is helped by the fact that TiVo is largely based on the Linux kernel. However, TiVo is not a general purpose computer and won't be running MythTV any time soon; it's a highly specialised device with an embedded processor and dedicated video processing hardware (which reduces the need for a high-performance main processor). TiVo recently launched a product that allows users to use the TiVo interface and features from a general purpose PC.
The TiVo business model of offering both the device and service for a cost has faced considerable competition from cable an satellite companies that offer similar devices and features, often for a lower price. TiVo still has a few unique features that set it apart from cable company devices, such as the ability to download a recorded program over the network, but only time will tell if these features will be enough for TiVo to remain competitive. It is worth noting, however, that TiVo recently won a lawsuit against EchoStar (Dish Network) for violating its patents. It is expected that other cable/satellite providers will soon follow suit and license TiVo's intellectual property. Despite these issues, TiVo as a company remains remarkably strong.
The TiVo device fills a niche market somewhere between users who are satisfied with cable/satellite company offerings, and users who don't mind the hassle of building their own systems from the ground up but want full control. TiVo's main focus is on ease-of-use and advanced features like "Season Pass" that are not present on cable/satellite company DVRs, and more recently partnerships with online video services.
TiVo has become a common house-hold name, much like "Kleenex" or "Xerox", and as such has cemented its place in common culture. TiVo devices are often referenced and sometimes make appearances in popular TV programs, including "Sex and the City", "The Daily Show with Jon Stewart", and "The Colbert Report".