What is the alternative to a vine ripened tomato?
Tomatoes grow on a vine. But it is possible to pick them unripe, ship them unripe (which is much easier than shipping ripe tomatoes), then gas them with ethylene at the destination. Ethylene acts as a plant hormone and causes ripening. 

But tomatoes ripened in storage don't taste the same as vine ripened ones. The compounds a tomato builds are dependent on the amount of UV light it gets, the surrounding temperature, the speed of ripening, the nutrients it gets during ripening, and many other variables. There are lots of tasty compounds it creates while ripening on the vine, which are absent when it ripens in storage. This is why vine ripened tomatoes are tastier. It is also more expensive to let them ripen naturally, therefore the producers label the vine ripened ones as a sign of quality, else customers wouldn't be willing to pay the premium.