The buy box maximization is a feature in the repricer which monitors your dynamic pricing, in combination with your seller status. It tracks continuously if you're the seller in the buy box, or another seller is.
As soon as you reach the buy box (which makes you the 'best offer') the repricer remembers the spot when you've reached that status, and freezes the repricer. It keeps your price at the same level, as long as nothing else changes in the offers of your competitors or your own pricing. In this way, you can avoid the situation that the repricer goes back-and-forth in your pricing.
For example: if you're not using the buy box maximization, and having a price of 5 euro, and do not have the buy box, the repricer will drop the price until your reach the buy box, as soon as you will reach the buy box, the repricer will increase your price again (to maximize your profits). This will continue until you lose the buy box, and then it will drop the price again. To avoid this back-and-forth effect, you can enable the buy box maximization.
Good to know: the buy box maximization only functions at its best when you're using the advanced scenario management of the repricer. In the normal situation, the repricer will drop your price below the competitor but does not check if you're having the buy box.
To use advanced features of the repricer you need to use scenario management, where you can decide what exactly needs to happen in which scenario (for example, if another seller has the best offer, or if you have the best offer).
To know more about the repricer, read this article.