When you start doing Chalices ... you will
I spent it willy nilly beforehand because I wanted to stay under 15 Insight at all times, but suddenly after the game ended and I got into Chalices I realized you can buy quite a few materials there and it is the only place you can get Coldblood Flowerbuds (aside from a limited small amount in Nightmare Frontier I believe).
For fun's sake, and taken from the Wiki, here is what certain amounts of Insight does:
0: The Witch of Hemwick will not spawn stalkers during the fight (not possible on first attempt). Use a Madman's Knowledge during the fight and she will immediately spawn stalkers.
1: Plain Doll comes to life / A group of Messengers appears in the Hunter's Dream next to the Plain Doll, granting you the Beckoning Bell and Silencing Blank as gifts.
15: Lamp enemies in Cathedral Ward will shoot projectiles. Scythe and Cross enemies' weapons have buffs. Gehrman in Hunter's Dream speaks when he's sleeping outside his house. Stalkers will spawn in Hemwick Charnel Lane, only after learning the password.
40: Lesser Amygdala become visible in the Cathedral Ward and other areas. This can also be unlocked by defeating Rom, the Vacuous Spider.
50: Hunter's Dream theme changes even before defeating Rom, the Vacuous Spider.
60: A baby's cry can be heard.
Gaining insight lowers Beasthood, lowers Frenzy resistance, and regardless of time of day (the story starts at Dusk and ends at Dawn) the more insight you have the darker it gets.