As a product designer you constantly have to make decisions about the product. Those decisions can be based on data, feedback or on the designers own experiences. The interpretation of feedback, data and experiences should be objective but often it is colored by the designers own believes and thoughts.
A cognitive bias is a deviation in judgment, where circumstances or thoughts can cause illogical decision making. When someone is cognitively biased they create their own subjective reality from their perception of reality. There are many different cognitive biases, but I will describe the ones most relevant for designers below.
The tendency to rely too heavily, or "anchor", on one piece of information when making decisions. For example when a company launches its product and their first customer gives feedback that something needs to be changed. The tendacy is to focus on that specific problem right away, while in reality it is just one of many pieces of feedback and would collecting more feedback be the better decision.
The tendency to do things because many other people do the same. This is happening all the time, especially at platforms like Dribbble. You see design trends coming and suddenly everyone is designing the same things, not because it is the best solution for their specific users, but just because everyone is doing it.
The tendency to search and focus on information that only confirms one's preconceptions. This happens a lot—guilty as charged—when you start with data driven design. If you want, you can always find a piece of data that supports the direction you want to go. Be aware.
The tendency to disbelieve or discard data or feedback that conflict with the expectations of the designer. It is hard to admit once you've worked hard on a design, that your users don't understand or like what you've made. The easiest way to deal with this is to discard this feedback or data. Often seen with younger designers—including my younger self.
When well-informed people find it extremely difficult to think about problems from the perspective of lesser-informed people. I believe this cognitive bias is one of the most widely spread biases in the startup scene. As a designer or product owner you have so much information about the product (what it's for, what it can and can not do, how to use it etc.) that it's almost impossible to see your own product from the perspective of a new user.
The first and easiest thing you can do to avoid a cognitive bias is being aware of this effect. Don't jump to conclusions too soon, think about how you make design and product decisions and realize your opinion might be as biased as any.