The team over at XDA-Developers is offering a pretty major bounty for the first person who is able to unlock the Samsung Galaxy S5 for rooting. Samsung, AT&T and Verizon won't offer a solution, and S5 owners are in their seventh week of waiting. This is basically seven years in the tech world, so fed up users pooled together their cash to create the bounty. Right now, its at $17,970 and rising. You can get $10,055 for Verizon's version, $7,915 for AT&T, or all the loot for a solution to both providers.
With root access, Galaxy S5 users can do a lot more cool stuff than their phone currently allows for; mainly the ability to install powerful apps and software. These things can allow users to do things like control battery usage, create automated backups, monitor the device remotely, and much more. Developers can even install their own custom version of the Android operating system. It is a seriously nifty feature to have, and especially important to the XDA-Developer community.
Rooting requires an unlocked bootloader (that's a program that loads the operating system onto a device) or other exploit that allows the developer to gain access to the Android Operating System software. (You really should be a developer if you're attempting a root, as one wrong move can disable your whole phone. Rooting your phone usually voids the warranty, too.) Verizon and AT&T locked the bootloader, so developers need someone to find an exploit. Samsung does have the power to get through those locks, but is not sharing it with users. Other device makers, like HTC, offer users directions as to how to get through those bootloader locks.