Similarly, if you're on 3 life and your opponent Lightning Bolts your face, this can save you. Of course in that case you could just run a regular Counterspell, but this does offer some extra versatility (such as being able to counter multiple spells, or the kind of tricks mentioned below)

Say you have made a token with Kiki-Jiki, Mirror Breaker. At the beginning of your end step, a delayed trigger goes on the stack, making you sacrifice the token. Now, if you cast Discontinuity in response, you end the turn, exiling the trigger and thus keeping the token. Those kind of tricks are mostly what this card is useful for

if you play this during your attack phase can you make your opponent unable to block? because i don't see why you would otherwise play this card during your turn.