Median means "in the middle". So, with regard to List Price, this means exactly half of homes listed are above this price and exactly half are below. For example, let's say there are 5 homes for sale in a market at prices of $175,000, $200,000, $250,000, $350,000, and $600,000. The Median Price would be the one in the middle, or $250,000.
Note that this is not the same as Average Price. Using the same example above, the average price would be $315,000 which is significantly higher than the median of $250,000. Statisticians might say that median is a better indicator of the "typical" home within an area because it is not affected by "outliers" (the $600,000 home in this example).
When selling or buying a home, the most useful information associated with Median Listing Price is the trend displayed in the graph. If the graph shows a downward trend, it means that sellers are dropping their prices in response to a softening market. A "soft" market is also referred to as a "cold" or "buyers" market. If Median Listing Price is trending down, it may take longer to sell a home and buyers may have more bargaining power. If Median Listing Price is trending up, the market may be "hot" and homes will likely be selling more quickly. Sellers will have the advantage when prices are going up.