Weather

Weather is an in-game phenomenon that mimics a Trainer's real-world weather experience. The current weather is reflected in the Map View and capture phase. Weather conditions make Pokémon of certain types to: Attacks of boosted types are more effective in Gym and Raid Battles, even if the user is not those types.
 * appear more frequently in wild
 * be at least level 6 and IV floor of 4/4/4 in wild
 * be level 25 and 13 in the Bonus Challenge of Raid Battle and Team GO Rocket respectively
 * award 1.25x Stardust when captured

Types of weather
There are eight types of weather conditions that occur in-game.

Extreme
If the weather outside is too dangerous, the game will issue a severe weather alert to notify the Trainer that they should seek shelter.

Full weather image: 

Trivia

 * This feature was announced along with Pokémon from Hoenn region on December, 2017, and released two days later.
 * Several weather conditions like Rain, Wind or Snow causes respective visual effects in Pokémon encounter screen.
 * Pokémon boosted by weather conditions appear with additional spinning, pale-blue rings beneath them in the Map View when they spawn.
 * That ring overrides the pink ring beneath lured Pokémon.
 * The same Pokémon spawn's CP level and IV will be updated as the weather changes. If the Trainer enters encounter screen before weather changes, the Pokémon will have originally spawned stats even if they are caught after weather changes.
 * This is possibly bugged for the once-per-day person Pokémon spawn, which seems to have its CP change according to weather, but reverts to original when caught.
 * Before the release of the Sinnoh Pokémon, weather had a higher effect on the rate at which Pokémon appeared.
 * The weather attack bonus can be stacked with shadow bonus.
 * If a Remote Raid Pass is used to join a raid invite from far away, at the capture screen, the gym's weather would be used instead of the trainer's location.
 * Unlike, Generation VIII games of main series in Pokémon GO, Fairy type is boosted with a cloudy weather instead of foggy one.