Agreed the website is poorly organized, but if you click About, you get that paragraph:

https://tvheadend.org/p/about

> Tvheadend is the leading TV streaming server and recorder for Linux supporting ATSC, DVB-C/C2, DVB-S/S2, DVB-T/T2, ISDB-T, IPTV, SAT>IP and HDHomeRun input sources. Tvheadend outputs HTTP (VLC, MPlayer), HTSP (Kodi, Movian) and SAT>IP streams, and can ingest multiple Electronic Program Guide (EPG) formats including over-the-air (OTA) broadcast data for DVB and ATSC, and OpenTV extensions like XMLTV and PyXML.

So it's a DVR project in the vein of TiVo and Windows Media Center.