Tethered

Tethered means being basically "attached" to your computer in a way; you must boot your device by running code on it to make use of an exploit.

iPod touch 2nd generation

The iPod touch 2nd generation was jailbreakable only as a tethered device until recently, when the hybrid dev team released the 0x24000 Segment Overflow, and the 2nd generation iPod touch became fully jailbreakable, permanently. The codename for the tethered jailbreak was Redsn0w.

Linux

Currently, certain devices are capable of booting to Linux. The downside is that this is a tethered boot.