There are a lot of different backgrounds in Baldur's Gate 3, and each of them has its own goals to achieve over the course of the story. By achieving these goals, you unlock something called 'Inspiration', which allows you to re-roll dice rolls to try again if you fail, and this can come in handy in almost any situation.
All Background Goals
Acolyte Goals
Saving The Heretic: Free the priest of Maglubiyet
Her Gift of Silver: Recover Selune's Treasure
Treefather's Sorrow: Unleash the full might of Silvanus
A Kiss Without Mercy: Please Abdirak
Silvanus Solitude: See the grove sealed off from the rest of the world
Last Rites Of The Dark Dancer: Obtain the blessed blade of Eilistraee
A Unified Spirit: Pray with the Flaming Fists
The Final Scribe's Boon: Find Jergal's Amulet
Tipping The Scales: Be worshipped by the Kuo-Toa
Fate Must Wait: Resurrect a party member
Justice Sees All: Find out why Anders betrayed Tyr
Shatter The Moon: Take out the protection guiding the Underdark fort
Divinity Undone: Read the Book of Dead Gods
Charlatan
Very Important Parasite: Decieve a Goblin camp guard
Cheese Your Way Through: Talk your way into the chapel
Merciless: Make the Flind eat itself
Silver Blades, Silver Tongue: Make Kith'rak Voss leave without any violence
Spiked: Poison the beer in the Goblin Camp
Mirror Master: Trick the magic mirror
Flexible Diplomacy: Betray the Tieflings that have captured Lae'zel
Anything For A Profit: Steal Crusher's Toe Ring without getting caught
Devil's Advocate: Interrogate the dead mind flayer without suspicion
A Better Offer: Convince the pit spiders to help you in the Goblin Camp
The Importance of Networking: Talk your way into the Zhentarim
One of Us: Use the hag's mask to get past her slaves
Just Passing Through: Trick the Moonhaven Goblins
Criminal
A Fine Fortune: Steal something worth 1000 gold
Friend Of The Family: Ally with the Zhentarim
Escape Artist: Escape from Jail
Slaughter's Prize: Ally with Minthara
Finder Keepers: Keep Barth's locket
Serpent's Bounty: Take Zevlor's Payment
Blood Price: Kill an innocent
Heretic: Steal the Idol of Silvanus
Open For A Surprise: Get the Zhentarim Iron Flask
Swiftly Stolen: Steal the Duergar Boots
Jailbreaker: Get Sazza out of the grove
A Sound Investment: Give Mol money
Culling The Crowd: Kill the drunk goblins with poison
Lesser Evils: Rob the enthralled fishermen
Entertainer
The Price Of Ink: Free Oskar the painter
The Art Of Agony: Perform for Loviatar
Life Of The Party: Toast with the Goblin Camp
Made You Look: Earn Mattis Respect
Celebrant: Dance with the Tieflings
Give Them A Show: Get the Goblins on your side while fighting Crusher
Chicken Chase Extraordinare: Win at Chicken Chase
A Bard's Muse: Inspire Alfira The Bard
Heart Of The Creator: Perform with Bernard the automaton
Feel The Beat: Perform on the Goblin War Drum successfully
A Story For The Ages: Turn someone to your side with a story
Folk Hero
Unmasking The Truth: Free a masked thrall
A Timely Rescue: Save Findal
The Most Unfortunate Gnome: Rescue the Windmill Gnome
Rescued From The Flames: Save everybody from Waukeen's Rest
Liberator: Liberate the enthralled fishermen
The Bard With Nine Lives: Rescue Volo In Act 1
Saved By A Thread: Save Smythin
Fate Worse Than Death: Save Liam
Guardian Of The Forgotten: Save the Tieflings from the Goblin's
A Lethal Endeavor: Escore Baelan out from among the Bibberbangs
Snake Whisperer: Protect Arabella
Protector Of The Small: Save Mirkon
Soul Warden: Save Nadira
Guild Artisan
In Working Order: Repair the Zhentarim hideout
The Spider's Gift: Identify the Drow armor near Waukeen's Rest
Treasure & Tramp: Find out what the Chest of the Mundane does
An Acquired Taste: Drink one of Auntie Ethel's potions
The Apprentice Turns Master: Make Nettie's Antidote
Valued Customer: Trade with somebody who thinks highly of you
A New Vision: Reforge the broken spear
An Artist In Need: Rescue Oskar the Painter
Mind Over Mushrooms: Gather Ingredients For Omeluum's potion
A Golden Masterpiece: Sell something worth 1000 gold
The Finest Masterpiece: Create a masterwork item
Regeneration: Fix the elevator in the Arcane Tower
Noble
Protector Of The Duke: Rescue Counsellor Florrick
Lest Ye Be Judged: Learn about Astarion's History
Noblesse Oblige: Dismiss a companion for interrupting a conversation
Soul For Sale: Acquire a Soul Coin
Blueblood Solidarity: Learn about Wyll's Family
Bodyguards For Hire: Recruit The Ogres
Eldritch Authority: Become a True Soul
Fine By Me: Bribe a guard
Dragon's Horde: Have a total of at least 2000 gold
A Man of Many Talents: Bring Volo to camp
Penchant For Diplomacy: Reach a High level of approval for a companion
Outlander
Nest Egg: Steal from the Carrion Crawler
Rock Steady: Survive the rolling boulder trap
Mushroom Enthusiast: Destroy one of every mushroom in the Underdark
Clever Cuckoo: Steal from the bird in the Underdark
Abyss Jumper: Get to the Underdark through the Well
A Noble Endeavor: Use a Noblestalk Mushroom
Sticky Fingers: Get the pouch from the spider crevice
Cub Tamer: Tame the Owlbear cub
Walking On Air: Use a fairy ting
A Mother's Fury: Beat the Mother Owlbear
Curse Breaker: Kill Yeenoghu's hyenas
Eyes Of The Wild: See the truth about the swamp
Sage
A Natural Alliance: Recognise the Druid and Harper armor
The Phases Unfold: Solve the puzzle sealing the Underdark door
Secrets Of The Matron: Read the Drow text
Reanimator: Bring Gale back using his instructions
The Forbidden Arcane: Read Omeluum's notes
Secrets Of The Sussur Tree: Read the Treatise on Anti-Magic
Secrets Of The High Chieftain: Read Volo's Guide To Goblins
Roots Of The Grove: Learn local history about the Druidic fresco
All Knowledge Is Worth Having: Read the Thayan Tome of Necromancy
Secrets Of The Shadow Druids: Read Faldorn's Canticle
A Solitary Spider: Read the Arachnomancer's journals
Secrets Of The Sundering: Read the Book of Dead Gods
Soldier
Pentacrush: Kill 5 enemies in a single run
Stalwart Heart: Get Rolan to stay
Chain Of Command: Follow the orders of the Flaming Fist at the Inn
Conquer The Conquerors: Defeat the Githyanki Raiding Squad
Crow Crusher: Kill every Goblin camp leader
Warrior Of The Hells: Kill The Cultist Leader that wants Karlach
Start Them Young: Inspire the Tiefling Children
Drowned In The Dark: Defeat the Ebonlake Duergar
No One Left Behind: Make sure all of the Grove's Defenders survive the first Goblin assault
Strategist: Kill a powerful foe in one hit
One For The Ages: Survive a fight where you kill ten or more enemies
Urchin
What Price Dignity: Steal the toe ring from Crusher without getting caught
Protect Your Own: Protect the child who stole Barth's locket
Born Innocent: Save the Owlbear Cub from the Goblins
Mercenary: Get coin from the Zhentarim survivors
The Allure Of Coin: Steal from the Harpie charmed child
Pyramid Scheme: Get the Ogres to work for you without paying them
Artful Dodger: Take Mattis' ring
Family Comes First: Get Meli to tell the truth
Not On My Watch: Save Arabella
Hunger Never Fades: Eat at Raphael's House of Hope
Slaying The Piper: Rescue Mirkon
Idolatry: Steal the Idol of Silvanus