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Memory and mental power.
Intelligence affects your Arcana, History, Investigation, Nature, and Religion skills and improves spellcasting for Wizards, Eldritch Knights and Arcane Tricksters (better chance to hit enemies with Spell Attack Rolls; increases the Difficulty Class of spells with Saving Throws).
Intelligence Modifier Chart
Baldur's Gate 3 uses the Point Buy ruleset.
| Ability score | Modifier value | Ability score | Modifier value | |
|---|---|---|---|---|
| 1 | -5 | 16-17 | +3 | |
| 2-3 | -4 | 18-19 | +4 | |
| 4-5 | -3 | 20-21 | +5 | |
| 6-7 | -2 | 22-23 | +6 | |
| 8-9 | -1 | 24-25 | +7 | |
| 10-11 | +0 | 26-27 | +8 | |
| 12-13 | +1 | 28-29 | +9 | |
| 14-15 | +2 | 30 | +10 |
Related Items
Increases Intelligence "to"
Warped Headband of Intellect sets 
to 17
Increases Intelligence "by"
Harmonium Halberd reduces by -1
+1 to Saving Throws
Circlet of Psionic Revenge only if Githyanki
Cerebral Citadel Armour Illithid Protection
Phalar Aluve Sing: 1d4 to [...] Intelligence Saving Throws
Advantage on Saving Throws
Aberration Hunters' Amulet Aberration Hunter: A Githyanki [...] has 
Advantage on Intelligence Saving Throws.
Fey Semblance Amulet Semblance of Fey: Advantage on Intelligence [...] Saving Throws.
Silver Sword of the Astral Plane Githborn Psionic Resistance: A Githyanki [...] has Advantage on Intelligence Saving Throws
Other
The Pointy Hat Glorious Pointy Hat: [...] bonus to Persuasion checks equal to your Intelligence Modifier.