Swimming allows light units to cross the river (during a bridge/ford battle) at any point. Mostly this means that if you're defending a bridge, you won't be able to just concentrate all your units on one end; you'll need to station some of your troops along the riverbanks to guard against swimmers. Otherwise they will be able to flank your defenders.
Countering swimming units is easy though, as it takes them a while to get across, they'll be very vulnerable to missile fire while in the water, and they will be tired/exhausted by the time they hit the opposite bank. And then there's the fact that they'd be emerging from the water in a disorderly formation and attacking uphill.
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