Brand bidding is a term used in compliance monitoring of affiliate programs, specifically on search engines.
Brand bidding occurs when an affiliate ads appear on search engines on specific keywords associated with a merchant (eg. their brand terms, for example "Commission Factory"). Usually when brand bidding, an affiliate is keyword bidding on a trademarked name, and is often therefore competing directly with the merchant. In some cases the affiliate may be bidding on generic terms on "broad match type" meaning that they may inadvertently appear on ads on a search engine (so unintended).
Your policies on brand bidding and paid search activity need to be clearly indicated in your merchant Terms & Conditions. The Commission Factory dashboard allows you to place restrictions on keywords that you want protected. Do this via the "campaign" setting in your merchant profile area, and enter the keywords that you want to restrict in the given area.
Some advertisers allow brand bidding to increase visibility on a more consistent basis. You may also choose to allow affiliates to use your brand name, limiting their usage to markets or search engines or groups of keywords where you are not active. For more information on how the benefits of partnering with this type of publisher, please read this article.