XYZ is a convention whereby the first 3 bids of a partnership's auction are on the 1-level (but not 1NT- over 1NT you can play some version of New Minor Forcing). SO, it goes 1-something, 1-something, then 1-of-a-major. After those 3 bids (1X-1Y-1Z), the typical treatment is to use:

 
2 by responder as an artificial relay. Opener must bid 2. 

2 by responder as an artificial bid, saying that the partnership is going to at least game.
Other bids by responder are natural and NOT Forcing; 2-level suit bids are typically weak, 2NT and 3-level bids are invitational.

Responder's 2 relay is used to either place the contract in 2, or to be followed by an invitational bid.

Examples below:

A]
1-1
1:

The responder can bid 2 to force opener to bid 2. After this, responder can pass to play there, or make an invitational bid (such as 2, which would promise at least 5 hearts). Responder can also bid 2 to set up a Game Force.
Other actions as above.

B]
1-1
1:

Nothing changes. Responder can relay with 2 or start a Game Force with 2. In both cases, of course, the 2-of-a-minor bid is completely artificial. 1 here would be natural and forcing (but NOT game forcing).

If using XYZ, it does not matter what the first 3 bids were, as long as opener's rebid is 1 or 1.

Of course, the major downside (other than forgetting) is that the partnership can't play in a 2 contract after a 1 opening.

As with any convention, the partnership must decide if this is on in competition (I recommend NO) or by a Passed Hand (I recommend NO).

This treatment has been steadily gaining in popularity since the turn of the millennium.