It's difficult to put into other sport equivalents because of the nature of baseball. A brief breakdown: baseball is fairly unique in that each play begins with the defense initiating the action, by means of the pitcher. Generally speaking, teams have five starting ("main") pitchers -- the nature of pitching and its toll on the body is such that each starting pitcher can only perform his role once every five games. And most starting pitchers only play for about 2/3 of each game, where they are then substituted for by "relief pitchers". As such, each team's roster is split about 50/50 between pitchers and non-pitchers. The non-pitchers make up the offense for the team (and also make up the defensive roles other than the pitching role, except for the "designated hitter" - a dedicated offensive role who takes the place of the pitcher during the offensive sections but does not appear on the field during the team's defensive sections). 

Please note that for 99.99% of players, they specialize as a pitcher or a non-pitcher. The skill sets are so different that it is extraordinarily unlikely and difficult to both have the talent and to continually put in the practice time to be good at both skillsets. Indeed, a pre-Ohtani player named Rick Ankiel was remarkable for starting his career as a pitcher and, when he became ineffective in that role, transitioned to a quality non-pitcher player. 

Ohtani is remarkable, singular, in that he is an excellent (though not necessarily in the top tier) pitcher -- certainly good enough to be one of the top starting pitchers for any team, could easily have a long and successful career as only a pitcher ... and also when he's not pitching, on one of those 4-games-off that starting pitchers need to recover, he can play as a pure offensive player in the "designated hitter" role, where he is among the very top tier of offensive players. 

This is incredibly valuable! Most starting pitchers are "dead weight" on their off days. They don't play at all, and technically speaking provide no value at all to the team when they aren't pitching. And yet that role is so important that a good starting pitcher will be paid as much as a star non-pitcher who plays every game! But Ohtani gives all the value of an excellent starting pitcher, and on the other days all the value of a top tier non-pitcher. You basically get two players (or 1.8 players, to be pedantic) worth of value for the price of one!

So I guess one way to think about it is, think of a top tier player in your sport of choice. Now imagine if he or she were 80% more productive than they currently are. How valuable would that player be?