Why galaxies merge:
When galaxies collide, the stars themselves will just stream by each other - remember how little of interstellar space is actually occupied by stars (e.g., if the sun is represented by a tennis ball in Tucson, the next nearest star is a tennis ball in Dallas). However, they do deflect each other by means of their gravity. The result is that a few stars are given very high speeds and may even escape from the system of two galaxies all together, while other stars are "slowed down" so they tend to fall deeper into the overall gravitational pull of the two galaxies together. Thus, when we say that the two galaxies merge, we are talking about most but not all of their stars. You can get a feeling for this transfer of kinetic energy to a minority of the stars while the rest of them merge from the simulation in the text, but an even better demonstration is in this simulation (caution!!! do not try over internet connection: 30 MB) (from J. Dubinski, http://www.cita.utoronto.ca/~dubinski/nbody/)
On the other hand, the gas clouds in the galaxies ARE big enough that they have a reasonable probability of colliding with each other. When this happens, they tend to cancel out each others motion (like two cars running into each other) and fall toward the center of the new system. As they are compressed into the center, star formation is triggered and a starburst begins. Cloud collisions can trigger star elsewhere in the merger also, before the clouds actually fall into the center. It is these processes that produce all the regions of new star formation in the merged system.