I'm working on a Hub on this very topic, in fact. It's a pretty fascinating finding, and I salute the astronauts who participated in the last Hubble servicing mission who made it possible.
As melpor said, it's nothing new. Astronomers have known for years that our galaxy and Andromeda were moving closer to each other. There was always a bit of mystery about the sideways motion of Andromeda, however - it was uncertain whether it would be a direct hit or glancing blow or near miss.
A good analogy would be a batter in a baseball game seeing a pitch coming his way. He knows it's headed in his direction and approximately how fast, but can't tell if it's going to be in the strike zone or will curve out of it. The new measurements from Hubble have given astronomers a much better understanding of that sideways motion, showing that it is likely going to be a direct hit.
When it happens, the night sky as viewed from out planet will be amazing. Too bad there will be nothing alive on Earth to see it.