Dave Meltzer explains:

The linear champion, a term used more commonly in boxing, is the guy who beats the champion to become the champion, regardless of specific belts recognized by sanctioning bodies.

... While Brock Lesnar holds that championship today, the linear title scenario isn’t as cut-and-dried. The UFC belt passed from (Mark) Coleman to Maurice Smith to Randy Couture, all in 1997. Couture then had money issues with the original UFC ownership group, left the company without being defeated, and went to Japan.

... Nobody beat (Fedor) Emelianenko until June 26, 2010, in San Jose, when Fabricio Werdum submitted him with an armbar in 1:09 in a Strikeforce match. So while Lesnar holds the most publicized version of a world title, Werdum actually holds the linear claim that traces back to (Ken) Shamrock.

-- Click here to see who are the champions in remaining major weight divisions of MMA.