What is the white swirl around the Pokémon on the map?

The white swirl you are seeing are Pokémon that are spawned whose type is related to the current weather in the new Dynamic Weather. You can check which weather is currently going on and see which types it will affect by clicking on the icon on the top right of the screen.

Below are the notes from the devs on what the Dyanmic Weather affects

Dynamic Weather Gameplay:

1. The Pokémon GO user interface will reflect each Trainer’s current local weather.
2. Certain Pokémon will be more likely to appear frequently in weather that suits them the most.
   • These Pokémon will yield bonus Stardust when caught.
   • These Pokémon are more likely to have greater potential in battle
3. Move types that match certain weather conditions will deal extra damage in battle

Basically, when you capture a Pokémon that spawned with the white swirl, you will obtain more star dusts and are more likely, but not guaranteed, to catch a Pokémon that is significantly stronger than normal. After a few days of testing of my own, the following are my findings of Pokémon affected by current weather

1. CP - On average, the Pokémon I have caught within the favored weather typically have much higher CP and are closer to being maxed out than those those who are not apart of the favored weather.

2. IVs - On average, a majority of these Pokémon have much better IVs as well. I caught Grass/Fire/Ground in the Sunny weather, and most of them had at least one maxed IV; if not, just a few points lower than max

3. Level (courtesy of this answer) - trainers are noticing an increase in capped capture level as well if caught in the favored weather. Previously, captured Pokémon was maxed a lv30 and no longer scaled with your level without having to power it up. However, if the Pokémon is caught in the favored weather, these Pokémon will no longer be capped at 30 and will further scale with your level.