OK, that was glib. Here's a real definition: A Stableford competition employs a points system that is set forth in the Rules of Golf under Rule 32. The Modified Stableford scoring system employs the same principle - golfers are awarded points based on their performance on each hole, with the highest point total winning - but with a different set of points than what is described in the rulebook.
A Modified Stableford scoring system typically awards more points for a great score on a hole compared to the rulebook definition of Stableford, while also including greater penalties (in the form of point reductions) for bad holes.
Modified Stableford is better known than Stableford because a former PGA Tour event, The International, was played using Modified Stableford. At The International, points were awarded on this scale:
Double Eagle: 8 points
Eagle: 5 points
Birdie: 2 points
Par: 0 points
Bogey: -1 point
Double Bogey or Worse: -3 points
That same point system went into use at the PGA Tour's Reno-Tahoe Open when that tournament switched to a Modified Stableford scoring system beginning in 2012. To be clear: golfers are simply playing stroke play in a Modified Stableford competition. But rather than writing down the number of strokes taken on each hole, the golfer writes down the number of points earned. If you make a birdie on a par-5, you don't write down "4" (for strokes), you write down "2" (because in the point values listed above, a birdie is worth two points).
(To see how this compares with the rulebook Stableford scoring, check out the Stableford definition.)
A Modified Stableford can have different point totals for different accomplishments as a tournament committee decides. It can also offer different points to different players for the same accomplishments.
For example, if handicaps are not being used in competition, they can be used to flight players into A, B, C and D. Then points are adjusted so that, as an example, a par gets an A player 0 points, a B player 1 point, a C player 2 points and a D player 3 points. It is more common, however, in amateur and recreational setting to use full handicaps in Modified Stableford and use net scores to determine points awarded on each hole.
For further explanation, please see: How to Play Stableford or Modified Stableford Competitions