Suppressing fire's purpose is to keep the enemy's head down and make it less likely to fire back. This is especially useful when one uses the "Cover Tactic" explained in Devin's Forum. The use of suppressing fire augments the defenses the team that's moving has for should anyone be in that location, they are likely to lose a large reserve of health or flat out die trying to pop out and kill your team mates.
One of the most common uses of this in real life is when a group of infantry is moving towards some type of building or emplacement that has some sort of known danger. If you watch "Green Zone" you'll see it used in the beginning. (Excellent movie, and while Fictional, is likely to be historical fiction)
Some excellent SF weapons would be any gun with a well aim reflex sight on full auto the F2K, Famas, or Tar. The M4 and M16 along with weapons with a similar layout are good for single fire use as they say maintain excellent accuracy in these conditions.