Okay so I have loved the Fire Emblem series so CE the GBA one. I went into this pretty blind and am absolutely overwhelmed by everything I just unlocked in the bonus box. What is any of this and should I be saving it for end gsme ?

The bonus box items are things you can use at your leisure. They're items you unlock as you increase your renown.

Bonus Teams - These are teams themed around former characters from Fire Emblem games. You can summon them and dismiss them from your game at will. Once summoned, they will spawn at a random cleared chapter where you can buy an item from them, pay to recruit them, or fight their team to recruit them. Once you have interacted with them once they disappear, but they can be summoned as many times as you'd like.

Bonus Items - These are one-off items that you receive simply for owning Fire Emblem and updating the game. You can redeem them once.

Bonus Maps - These are special Paralogue missions that can only be attempted once you have completed Chapter 25 of the main story. They are significant challenges and allow you to recruit special characters if you follow the correct steps when completing them. You can activate them at any time to place them on your map, then attempt them at your leisure. Once completed, their stores will sell you high quality weapons.

Bonus Challenges - These are challenger sets for the multiplayer Double Duel mode. I haven't actually played multiplayer so I can't speak to the specifics about these, but I imagine you'd be welcome to use them whenever, wherever you had someone to play with.

EDIT: TL;DR Activate the Bonus Items and Bonus Maps immediately, activate the Bonus Teams whenever you want to use them, and the Bonus Challenges are only relevant if you're playing multiplayer.

Actually the Renown Awards are completely separate from the Bonus Box :D

@starvinggamer: Yeah, you're right. Frankly, there's so many bonuses in the game that it's hard to keep them all straight. :P