Behavioral segmentation, as the name suggests, focuses on the actions users have taken. Examples of behaviors marketers may want to segment on include item/category/brand purchased and item/category/brand browsed on site.
Nothing particular about a customer's demographics causes them to buy a particular product. You might imagine two neighbors, both with the same gender, age, ethnicity, and income level, who have completely different purchasing habits and preferences. In that sense, behavioral segmentation goes a step further than demographic segmentation in that it doesn't segment on a proxy for behavior, but segments on behavior directly.
Segmenting on behavior is only possible if you've captured some sort of user behavior. As such, it is much better suited for retention than for acquisition. It can be tempting to continue to push for the same type of behavior from your segments, but behavioral segmentation lets you figure out true similarities between customers and can be used to encourage new behaviors as well.
One thing to watch out for when doing behavioral segmentation is the temptation to segment on whether a customer “has ever” done something. Segmenting on “has ever” can lead to biased results that may not be initially apparent. The root of these biases lies in the fact that a customer is more likely to have done something if they've made more purchases. For example, a customer who has made ten purchases is more likely to have bought Item X than a customer who has only made one purchase, so of course the “has ever purchased Item X” segment will have generated more revenue for you over their relationship with you than the “has never purchased Item X”. A way to get around this bias is to segment on a particular behavior associated with the first purchase or with the most common purchase. This normalizes the behavior since every customer will have made a first purchase and every customer will have made only one first purchase.