Jailbreaking is pretty much removing the restrictions placed on the devices by Apple.
Is jailbreaking bad?
No.
It doesn't make your phone slower in any way (the tweaks you use are the ones that do).
It can be bad, though just not to you.
Some tweaks like LocalIAPStore are used by some jailbreak users to "steal" money from devs by stealing In-App Purchases (gets them for free). There are even more tweaks out there that do more bad stuff.
For warranty, you can just remove the jailbreak and restore your device, they won't even know it was ever jailbroken.
For everyone saying you could destroy your iDevice:
The same way goes with a Windows computer, if you download something stupid (maybe like a virus) or delete System32 (you can't), Windows breaks.
The good side about iPhones though is that there is a built in SafeMode feature that disables all tweaks and allows you to fix your phone by removing a bad tweak and if that doesn't work, you can always restore your phone again instead of having to pay $200.
