Swarms are Pokemon that are usually rare or even not available for that region that appears suddenly with swarms of that Pokemon on a certain location.
Examples:
DPt - Professor Rowan's assistant Dawn/Lucas's sister will tell you the swarms of the day,
including Snubull, Smoochum etc...
HgSs - Prof. Oak's channel broadcasts the swarms of the day, including Luvdisc, Swablu,
Chansey etc...
BW/BW2 - Bulletin Board from across the Unova region Gates annouces the swarms like
Volbeat, Minun, Hippowdon etc...
RSE - TV broadcasts the swarms like Lotad, Skitty etc...
Most games requires the player to complete the main story game to activate this feature.