Custom events are a type of conversion goal, which are customer actions on your website that you want to track. Custom events require a UET tag — for more information on UET, check out What is UET and how can it help me?
Why custom events exist: When you add the UET tag tracking code to your website, it makes a call to Microsoft Advertising every time a user visits that page. You can then define conversion goals to record visits to particular webpages (thankyou.html for example) as conversions. However, you might have webpages that drive more than one type of conversion. For example, you may allow people to both subscribe to a newsletter and download a white paper on the same webpage. In such case, it is insufficient to just know that someone visited that webpage if the goal is to track the subscriptions and white paper downloads as separate conversions. That is where custom events come in. Another example would be that you have "click out" from your site to other seller's pages or websites that you refer traffic to. Since you don't have permissions to implement tags on those sites, you can track how many times you send a customer to another site via custom events.
Some examples of using custom events:
Get started: How to track custom events with UET