LNB's and LNBF's are both amplifiers used in satellite dishes. As with other signal amplifiers, they take the very faint signal they receive and magnify it so that it is powerful enough to use. This is the first step in taking the microwave signal coming from space and turning it into images and sounds for televisions and computers.
A simple LNB attaches to the feedhorn of a satellite dish. An LNBF is a more highly developed piece of technology, being a part of the feedhorn itself. For this reason, an LNBF can be smaller than an LNB with comparable capabilities.
As you switch channels, the LNB switches polarity through the use of an exterior motor. With an LNBF, the polarity changes when the receiver changes the voltage going into it. This voltage shift causes it to switch back and forth between two different antenna probes (horizontal and vertical) within the LNBF itself.
Larger, older satellite dishes generally use the older LNB's that are separate from the feedhorn. Smaller, newer satellite dishes generally use the more compact LNBF's. Because the industry has shifted almost completely to the use of LNBF's, many actually do not even make the "F" distinction anymore, as LNBF's are completely replacing LNB's anyway.