Subtitles are the text that appears in the bottom of the screen (or other such display area) on television programs, movies and like. They're often a translation of the dialogue to other language (usually the principal language spoken in the country the program is shown in), or transcription of the text in original language.
In regards to picture signal, the subtitles are often either "burned" on the video signal, or distributed via separate channel as an overlay to the picture. Analog systems (such as plain old TV and, by extension, analog video tapes) tend to send subtitles the first way, and digital systems (digital TV, DVDs and some other systems) tend to do the latter - with exceptions, of course. The advantage of the separate subtitles is that multiple sets of subtitles can be used, and the texts can be removed completely if so desired; The disadvantage of the burning is that it can't be easily removed!
Computer and video games tend to use the overlay system, for obvious technical reasons =)
In movie world, the subtitling is often added to a normal film print with specialized machinery. (I've seen this kind of machine at work once in Finnkino (?), but I'm not sure exactly how it worked. My impression was that it added a wax coat of some kind? I have to do more research on this subject...)
Subtitles allow for more exact translations than dubbing in many cases - no need to stay synchronized with the lip flap (⇒lip synch), and you can put more details there.
Subtitles, especially digital ones that can be turned off if so desired, are superior to dubbing for many reasons. For a nice comparison, ⇒Subtitled or dubbed?
The only complaint I usually have is that the translation quality - even though badly translated subtitles are less annoying than badly done dubbing! The translators (at least in Finland) seem to fall into routine of some sort, and as a newbie subtitler, that was an easy trap for me, too; Tricky translations are sometimes left into less than desired form. The translators need to be familiar with the terminology and culture of the translated material, and this isn't always true, as regrettable it may be.
Also (as Albert Herring told me) in many places subtitlers get paid less than translators of other material, and thus people who do that would rather do something else. A shame, really, considering the importance of the field.
I personally think that translators should always keep in mind that they're not doing an "interpretation" of artwork; they're doing part of the artwork, part that makes it accessible for many people.
How to roll your own?
I do "fansubs", but my fansubs have nothing to do with Japanese animation =) I ocassionally subtitle Finnish programs in English just for heck of it (and to show the otherworldians what sort of audiovisual things are happening here...).
There are many programs for subtitling; My own personal choice is Sub Station Alpha, a freeware program for Windows. It allows you to examine a .wav (extract the soundtrack as a .wav from VirtualDub, convert it to 8-bit 11025 mono, and scrub around in SSA!) and write subtitles easily based on sections of the .wav.
Many programs (including VirtualDub's "subtitler" plugin that burns subtitles - and also probably some tools to subtitle MPEG 2 do this?) read SSA scripts.
You can do it with any video editor that can add text, but that can be painful =)