When people talked of PC TV software/tuners or even generally TV Tuners a few years ago they were usually referring to a piece of hardware that you needed to plug into another device to enable it to function as a TV.
Some of the earliest hand held consoles also had TV tuner options available for them that enabled them to work as functional portable TVs, however, these early tuners were really expensive, the quality was questionable and they could only pick up the basic TV stations available in the surrounding area.
As TV tuners advanced the quality improved and the number of devices that could work with tuners increased rapidly but for a long time the price of this equipment remained high. For a brief period of time these tuners were included as additional hardware powered functions in mobile phones to allow them to pick up stations and let people watch TV on the go.
The true evolution of the TV tuner has come recently and been enabled by an increase in affordable bandwidth and Internet access speeds. The modern TV tuner no longer needs to be plugged in (as hardware) to another device and can be much more easily downloaded as a piece of software that can be run on a basic operating system. Traditional tuners could only function if you were in an area with a fairly strong analogue TV signal, however, today’s software tuners function by sourcing the media you desire online and allowing you to stream that to your monitor (or other display device depending on your setup). This new type of tuner is usually referred to as of the "streaming software" generation rather than the "hardware generation" which was the original plug in incarnation.
The software generation of tuners main differentiation from the traditional model, other than it is installed rather physically plugged in is that it does not pick up the signal from the airwaves, it instead relies on an existing data connection to pull a stream from the Internet. This meant that early software tuners were only available for the PC but and that the system needed to be wired to the Internet (as was the only mainstream method of connection 10 years ago) but once again, as with the traditional tuners, this has now evolved so that they can be used with mobile devices that can run a basic operating system!
The main issue/obstacle early mobile devices had with the modern tuner was the fact they needed a fast, reliable and affordable data connection, which, to start with, meant that they needed to be wired in somewhere and therefore this took away the wirelessness of the device! As the technology to facilitate the fast wireless connections became more common the technology became feasible but network restrictions on data usage and the high cost of data were the next barrier. Finally, in 2012 with many unlimited data plans and handsets that can provide fast connections the software TV tuner is as feasible on mobile devices as it is on standalone PCs.
Back when TV tuners were first invented a lot of the appeal was that you could use them to change a device you already owned into a TV and thus not need to buy a TV, for example people with a PC would be able to buy a tuner and not need a main TV. People with a mobile games console would buy a tuner and turn their console into a portable TV avoiding the cost of an expensive TV and also dodging the inconvenience of having to carry two fairy bulky devices round.
In 2012 the price of TVs has dropped considerably and you can quite easily watch TV on a mobile phone, the appeal of a traditional tuner has more or less gone away but PC TV tuners are still really in demand but for a different reason.
Modern software tuners allow you to connect to streams online that you would otherwise not be able to find or not be allowed to access, these streams are often premium channels and content that you would normally have to pay a high monthly fee to view and in some instances what you can access may be totally unavailable in your country. Sporting events shown on pay per view can often be streamed online through a modern tuner at no cost.
Sports fans are probably group of people who are most familiar with the use of streaming tuners and Internet TV software in general as it is possible to watch almost any game live using a high quality tuners and while movies, shows and pretty much anything else can be viewed with a little searching sports seem to be the main angle the tuners marketing departments seem to push them on.