Generally most of the distance from the headend to your house on modern cable systems is fiber. They basically use fiber most of the way and then use something called a node which converts the fiber to coax (regular cable lines). This is then distributed to your house, along with many others and may be amplified a few times depending on how far you are.
Fiber optic cable is definitely better. It is not susceptible to noise and signal attenuation (loss) as regular coaxial cable is. It is also less attractive to cable thieves as it does not contain copper. It also can carry much more information than coaxial cable. The downside is that it is more expensive to deploy and the active equipment on each end of a fiber link can be more costly than coax. It also requires special physical handling, i.e. there should not be any sharp bends in the cable. Many cable companies aren't interested in going fiber all the way to your house because it would cost them a lot for an uncertain return, and there are technologies such as DOCSIS3 which can squeeze more life out of an existing copper cable plant with minimal investment.
From a customer standpoint, if they are going to deploy fiber all the way to your home, you can expect faster internet speeds and more HD channels, like Verizon FiOS is doing. They may have to install a box called an optical network terminal or ONT which converts the signals on the fiber to coax or cat5 cable.
But most cable companies really aren't going to put fiber all the way to your home. What they are doing is increasing the amount of fiber in the network but the signals will still be delivered to you over regular coax. The most common thing that cable companies are doing are node splits which means that if a node has 500 people on it, they may make 2 nodes and put 250 people on each node. This has great benefits for internet speeds (since the bandwidth is shared) but doesn't really do much for TV.
I suspect your cable company may be just using fiber as a marketing term. Cable companies have been using fiber for many years now (since the 80s in fact) but recently due to competition from phone companies with brand new all fiber networks they are pushing fiber deeper and deeper into the network.