This answer assumes the games in question are Scarlet and Violet, unless otherwise noted. Details between other games may differ from what is shown here.
Harsh Sunlight
Boosts the amount of HP Synthesis, Moonlight, and Morning Sun heal.
Thunder and Hurricane have 50% accuracy.
Solar Beam and Solar Blade become one-turn moves.
Growth boosts Attack and Special Attack sharply.
Sandstorm
- Shore Up restores more HP.
Rain
Snow/Hail
Permits the use of Aurora Veil.
Blizzard gets perfect accuracy.
[Diamond and Pearl] Blizzard has a 30% chance to hit through Protect or Detect when used in hail.
Fog
[Gen IV] Weather Ball's power doubles.
[Gen IV] All moves set to 3/5 their original accuracy.
[Legends: Arceus] All moves' accuracy decreased by an unknown amount.
[Only in games with Desolate Land] Extremely Harsh Sunlight
- Prevents the use of any Water type move. This includes Natural Gift with a "Water" type berry.
[Only in games with Primordial Sea] Heavy Rain
- Prevents the use of any Fire type move. This includes Natural Gift with a "Fire" type berry.
[Only in games with Delta Stream] Strong Winds
- Forces moves that are super effective against Flying types to deal neutral damage.
[Pokemon XD: Gale of Darkness] Shadowy Aura
- Weather Ball's power doubles and becomes a typeless move.
Snow/Hail, Sandstorm, Rain (and Gen IV Fog)
Morning Sun, Synthesis, and Moonlight restore less HP.
Solar Beam and Solar Blade have their power halved.
Harsh Sunlight, Sandstorm, Rain, and Snow (Hail)
- Weather Ball's power doubles and changes to a different type depending on the active weather.
[Only in games with Desolate Land, Primordial Sea, and Delta Stream] Extremely Harsh Sunlight and Heavy Rain
- A Pokemon afflicted by Powder that attempts to use Sunny Day will take damage.
[Only in games with Desolate Land, Primordial Sea, and Delta Stream] Extremely Harsh Sunlight, Heavy Rain, and Strong Winds
- Prevents the use of Sunny Day, Rain Dance, Sandstorm, and Hail.
Weather (Bulbapedia)
Electric Terrain
Grassy Terrain
Halves damage taken from Bulldoze, Earthquake, and Magnitude.
Grassy Glide has increased priority.
Floral Healing restores more HP.
Misty Terrain
Grounded Pokemon take half damage from Dragon moves.
Misty Explosion's power increases by 50%.
Grounded Pokemon can't be affected by non-volatile status conditions.
Grounded Pokemon can't be afflicted with confusion.
Psychic Terrain
All terrains
Terrain Pulse doubles power and changes type based on active Terrain.
Steel Roller only works when a Terrain is active.
Nature Power turns into a different move depending on the Terrain.
Secret Power's effects differ based on the active Terrain.
Camouflage changes the user's type based on the active Terrain.
Defog, Splintered Stormshards, and G-Max Wind Rage clear the active Terrain.
Terrain (Bulbapedia)