Swim allows the character to move through water tiles more easily. It normally costs 2 Action Points to move through a water tile, but the Swim skill reduces this cost to 1 Action Point.
Furthermore, the character will no longer gain the Swimming Status Effect nor the Treading Water Status Effect upon entering water and thus cannot drown. Some terrain that can be interacted with in a swimming-like way, such as the Lake of Fire in Stygia, will still deal damage and can thus kill you in other ways.
If a character without this skill with the Treading Water Status Effect moves into a new water tile, they will lose the Treading Water Status Effect and regain the Swimming Status Effect. Leaving water will clear any swimming- related Status Effects from the character.
Note: Even with Swim, a character will not regenerate AP on water, lava and void tiles, so running out of AP when traversing such terrain is highly inadvisable and will result in drowning.