|MythTV is software that runs on Linux to make a computer into a DVR. Visually it looks and acts like any on-screen menu you've seen, except not as "arty" as most DVD menus. There are screens that let you navigate through the various functions using a TV remote control. MythTV has the usual tv-watching and -recording functions, and a collection of plugins for other things like music collections, slideshows, the weather, web browsing, and more. Behind the scenes, other programs deal with recording and processing recordings. One program grabs guide listings. Another flags commercials.
Here's a very simple diagram of the usual "stack" of software/hardware for typical MythTV systems.
| At Another Computer
|| In Your Comfy Chair
|| Around the House |
||TV & Remote
||MythWeb / media player|
Storage --> Screen | Storage --> Network | Storage --> other format for download
TV Provider --> TV Tuner --> Storage + Database
schedules source or EPG --> Database
Storage --> commercial flagging --> Database
Storage --> transcoding --> Storage
|CDs, DVDs, Internet
||Antenna, Cable, Satellite|
MythTV has two sides which may be combined on one computer or distributed over several computers.
MythBackend is the central hub of MythTV operation, managing all recording and playback of content. It collects data from your TV input(s) and stores it on disk, making database entries for each program about its details and possibly metadata like actor's lists and even artwork like movie posters. It also uses the database for music and video collections. Most setups have only 1 MythBackend but it is possible to have other "slave" backends that can record from other sources or flag commercials. A MythBackend will have TV tuners attached, and large hard drives to store content.
MythFrontend is the software you use to talk to MythBackend - it displays what's been stored about content and ultimately the content itself, in addition to letting you manage that content. A MythBackend can have a MythFrontend on it to put everything on one computer, but other machines can be made into MythFrontends and then networked to allow access from other rooms. A frontend can be made from a very simple machine, possibly even one small enough (without a hard-drive or fans) to be tucked behind a display.
It's also possible to use other devices that can talk over a network to the MythBackend like tablets or game consoles or "TV box"es to play content. Or even just another computer without a MythFrontend using a web browser or media player. These players can only play - without MythFrontend they won't be able to manage content. MythWeb through a web browser can do both playback and some management and is especially handy for managing recording schedules.