I think that fit-showing jumps (FSJ) are one of the most useful competitive treatments out there. With many of my favorite partners, I play these jumps in almost all competitive situations.
The basic fit-showing jump is a fairly simple concept. When your partner bids a suit and your RHO takes an action, a new-suit jump by you shows invitational values, length and strength in the bid suit, and a fit for partner. For example, let's say I hold 742 A76 KQJ93 94. My partner opens 1H, and my RHO bids 1S. Most folks would just bid 2S, showing a limit raise or better in hearts. Playing FSJs, I leap to 3D to show this hand. Let's give partner two sample hands, and see what he would do on the two auctions.
(A) A53 KQJ84 A87 52
(B) A53 KQJ84 52 A87
Of course, with either hand, over 1H (1S) 2S (P), partner will take the same action (if it was me, it would be bidding game at IMPs and signing off at matchpoints, but wouldn't be sure if either was right), but over a descriptive call like 3D, partner can confidently bid game on (A) and confidently sign off with hand (B).
Of course, as with any convention, we need to ask ourselves "what are we giving up?" Here, to play FSJs, we're giving up strong or weak jump-shifts, whichever your partnership is currently using.
A strong jump-shift should be a hand like:
AK AQJ864 KJ3 J2.
Over your partner's one of a suit opening and an overcall, you jump in hearts to show a powerhouse with long hearts.
A weak jump-shift should be a hand like:
85 KJT864 963 52.
Over your partner's one of a suit opening and an overcall, you jump in hearts to show an awful hand with long hearts.
Most tournament players long ago dropped the "standard" strong jump-shifts in competition in favor of the weak jump-shift. They noticed that the weak hands came up far more often than the strong ones, and, especially with the rise of Two Over One Game Forcing, the big hands had many other ways to show strength and get information out of partner.
So they moved to weak jump-shifts, in large part (in my opinion) because there weren't any other widely-publicized alternatives. I played them for a while, but noticed that even when the right hand for a weak jump-shift came up*, two or three of my long suit wasn't always the right contract. In fact, it'd often give the opponents the fielders' choice of doubling me or bidding to their best contract (remember, they've already shown values and shape on your right). So when someone explained FSJ to me, I was an overnight convert.
*Also, my partners would often not wait for the right hand to come up to make the weak jump-shift... giving the opponents even more of a fielders' choice.