Hi David a free floating barrel is a barrel that is only attached to the reciever of the firearm. The stock does not touch it anywhere along its length. It's purpose is to maximize the accuracy of the firearm by not letting the stock interfere with the natural frequency of the barrel as the bullet passes through it thus maximizing accuracy.

A free floating barrel means that the barrel is mounted directly to the receiver and does not actually touch the stock at any point. This helps with the harmonic balances in the barrel when shooting. Ultimately, this helps with accuracy. As the barrel heats up, if the stock were touching it, it could slightly alter the barrel and can lead to inaccuracy after repetitive shots. Obviously, there are plenty of rifles out there without free floating barrels that are plenty accurate. Hope this helps.