Anchoring or focalism is a cognitive bias that describes the common human tendency to rely too heavily on the first piece of information offered (the “anchor”) when making decisions. During decision making, anchoring occurs when individuals use an initial piece of information to make subsequent judgments. Once an anchor is set, other judgments are made by adjusting away from that anchor, and there is a bias toward interpreting other information around the anchor.
For example, the initial price offered for a used car sets the standard for the rest of the negotiations, so that prices lower than the initial price seem more reasonable even if they are still higher than what the car is really worth.
http://en.wikipedia.org/wiki/Anchoring

Examples of Anchoring Bias

1. An investor will have an attraction towards a stock which has fallen considerably from their previous or all time highs – say even from a 52 week high. The investor is anchoring on the high prices that the stock had reached and now believes this provides an investment opportunity. If the fall is due to overall market sentiment and not due to any deterioration in business fundamentals then the investor has made a right decision. But, if it is otherwise the investor will stand to lose a substantial amount of capital soon.
2. Few times investors also would anchor to a price only below which they will buy. By this, they may miss the opportunity to invest. For instance, someone may want to buy stock X at Rs 200 or below but the price moved to Rs 250 and hence wanted to wait to come down to their anchored price (Rs 200). But, the stock further moved up to 300 and then 400. The investor would never buy that stock and in next few years it would have reached 1000 or even more. Here, clearly the investor has missed the opportunity. He should have only checked the fundamentals and margin of safety and if the price was right even at 200, should have bought it.
3. Similarly, investors will hold on to a price for selling. They want to sell a stock only if it reaches a certain price or a target (all time high etc.).
For example, an investor has bought a stock at Rs.500 (which has fallen from its all-time high of Rs.1000). He may anchor his price at Rs.1000 to sell the stock. Even if the price reaches 800, the investor will not check the fundamentals and compare to the current price and decide to sell. He may just hold on to it to reach Rs.1000. But, the stock may fall to 500 and 400 and 300, but he may not sell and instead may accumulate more to sell at Rs.1000, the price which the stock may never reach in a decade too.

How to save from Anchoring Bias

1. Just understand that these types of biases exist and evaluate if you are caught in this bias
2. Just be patient and check once if you are making an emotional decision or a data driven decision
3. Discuss with trusted resources, even to be specific ‘devil’s advocates’ to take a critical thinking view
4. Check only the underlying fundamentals and if it is a great business, go ahead and buy, even if you have a reasonably fair enough margin of safety. Because, great businesses very rarely trade at mouth-watering valuations. Moreover, they will always trade at higher valuations, because of its future prospects derived from its moat and durable competitive advantages.
Adapted from Safalinvestor.com