Fibonacci retracements are technical indicators that help predict when, and to what extent, price reversals are most likely to occur.

Leonardo Pisano Bigollo (aka Fibonacci) was a mathematician from Pisa who introduced the Fibonacci sequence to the West in the 12th century. It is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 and so on to infinity.

• In technical analysis, a Fibonacci retracement is created by taking two extreme points (usually a peak and a trough) on a stock chart and dividing the vertical distance by the key Fibonacci ratios of 23.6%, 38.2%, 50% and 61.8%. Once these levels are identified, horizontal lines are drawn and used to identify possible support and resistance levels.

• A number divided by the previous number in the Fibonacci sequence approximates 1.618 and a number divided by the next highest number approximates 0.6180. It’s known as the “golden ratio.” Once prices break below 61.8% they immediately begin a new leg up so it prevents an investor from selling at the wrong time and to prepare to buy on the dip.

• 0.3820, the next most significant number, occurs when you take one of Fibonacci’s sequence numbers and divide it by another one two places higher. For example: 13/34 = .382. 

• The 23.6% ratio is found by dividing one number in the series by the number that is three places to the right. For example, 8 divided by 34 equals about 0.23529.

"Fibonacci retracement levels are horizontal lines that indicate the possible locations of support and resistance levels. Each level is associated with one of the above ratios or percentages. It shows how much of a prior move the price has retraced. The direction of the previous trend is likely to continue. However, the price of the asset usually retraces to one of the ratios listed above before that happens." Investopedia 

The following chart illustrates how a Fibonacci retracement appears.

Fibonacci retracement analysis deals in probabilities here, not certainties - there are no guarantees -  so it is always a good idea to confirm your results with other technical indicators before actually doing any buying or selling but, that being said, using such a technical analysis tool can help you better understand price trends and manage risk.