It's not a well-known term on the game, so you're best to ask the team leader or team admin what they mean by it. Based on the context you've given me, it sounds like the last Monday of the month is when the team breeds horses to sell.

Breeder's week is when team members are given top preps to skill for prix

Prix teams sell their top teared foals either in direct sales or to players who have placed an order for a prep. In order to keep customers coming back most teams have a rule that team members aren't to use top/current teared horses for personal use in the Prix. If they want to enter they need to produce their own prep in the days before team tearing is done. Really wouldn't be fair to all the players who payed passes for horses only to see team members beat them.

But team members do deserve to compete in Prix for all their hard work so one week out of the month (called Breeder's week) they get to keep the top teared foals for themselves (or sell if they chgose not to enter Prix).

Oh i see! How interesting. Thank you all for your responses.