From the Wiki entry:
"Anchoring or focalism is a cognitive bias that describes the common human tendency to rely too heavily, or "anchor," on one trait or piece of information when making decisions."
The notion of Anchoring Bias comes from Cognitive Psychology, not from Logic.
I suppose it could be a fancy way of saying that sometimes we cannot see the forest for a single tree, and are thus "prevented" from considering all of the relevant facts or options.
This sort of cognitive bias typically operates, as do most biases, unconsciously or reflexively, as a gravitational pull towards some decision or reaction.
A true example (but not an unconscious one, from the Mrs., on considering what new car to buy): "It just has to be the right shade of maroon."
Another example, reported to me by a pediatrician friend: "I ordered a brain MRI ($800) for a 10 year-old kid with tension headaches. Totally unnecessary, and I realized afterwards that I did it because I had read a journal article over the weekend about an undiagnosed brain tumor in a 10 year-old."
Thus, like most fallacies and biases, it's part of the brain's effort to be efficient or persuasive in its heuristics by tossing out an anchor on one detail (ouch - that's bad writing), and often might, but doesn't always, lead to the most realistic choices.
As we learn more about how our brains make decisions outside of our awareness, being aware of, and being able to monitor, the shortcuts our brains take should serve us well.
I could not resist this free association, having recently learned that "Anchors Aweigh" was written in 1906 to be a swinging football song (which it is):
