Fusion Voting helps move the main parties in certain directions.

Let's say the Working Families Party wants to shift the tax burden off user fees and sales tax, and increase the income tax to make up for it

The WFP goes to a Democratic candidate and says "Hey, we'll endorse you on our party line, and our party members will vote for you, but only if you promise to back our tax plan". If the Democratic candidate wants votes from that minor party, they might say yes and accept the endorsement.

This helps allow groups of voters to apply pressure on the major parties outside of the primary process. If one of the two major parties selects a candidate who is too extreme or too moderate, they might alienate one or more of the minor parties.

If you're a voter that's conscious about specific issues, and you find a minor party that cares about those issues, you can vote across their fusion line knowing they already did the work to vet candidates that support those issues.