That is right, we are on a collision course with our neighbor, the Andromeda galaxy.
We are hurtling towards each other at 250,000mph, though considering the size of each galaxy and the distance between them that is basically a stand-still. In about 4 billion years however you can expect the sky to be very different as the Andromeda galaxy gets closer and eventually collides with the Milky Way. The Earth (and almost every solar system) will be fine, because there is just so much interstellar space for everything to pass right by. The interstellar gas will collide however and start new star formation, this will be noticeable in the sky as all of the new giant-balls-of-hydrogen (i.e. stars) begin to ignite. Eventually, the cores of each galaxy will merge and dominate the night sky.
See the entire process here via Science at NASA