So the Milky Way and Andromeda are moving through space like our space ships do when they go to the space station, is that what you are saying?
If so what is the mechanism for such movement?
The two galaxies are
in orbit around each other, ICANT. The mechanism is something called
gravity, which is involved in other orbiting things, like the Earth and its moon. As there are at least a few dozen galaxies, three of them of comparable size, in our Local Group, the orbits are more chaotic than the ones in our Solar System. This is why an eventual collision is in the works.
2,500,000 light years is pretty dang close on the scale of the observable universe. I personally have seen an object, 3C273, that's about a thousand times as far from us as the Andromeda galaxy is - and that with my 6-inch reflector. On that sort of scale, galaxies/clusters of galaxies are moving apart. On local scales, like a piddly 24,000,000,000,000,000,000,000 meters, gravity can dominate that overall expansion.
"The Christian church, in its attitude toward science, shows the mind of a more or less enlightened man of the Thirteenth Century. It no longer believes that the earth is flat, but it is still convinced that prayer can cure after medicine fails." H L Mencken