All stables have equal potential to train or breed a future champion of any distance or style. Maybe, though, you might decide that you'd like to specialise your stable in a particular area, improving your potential slightly in certain areas. Specialist Facilities will help you do just that.
Firstly, Specialist Facilities are expensive! They are not something that a new stable should be concerned about immediately. Every stable will function perfectly well without these extra facilities, and the bonuses they provide are only a small enhancement to the 'standard' performance of a stable.
If you have the spare cash to build a Specialist Facility, then you can install your Facilities on the 'Facilities and Training' page, accessible from anywhere in your 'Stables' Menu. From this page you can investigate the list of Specialist Facilities and decide which ones you might want from looking at the relative costs and benefits of each Facility. Each stable may only have 3 Specialist Facilities at a time, so choose wisely!
Each Facility in your stable has a 'Condition', which will rise or fall over time. The condition shows you how well the Facility is functioning, and what level of benefit it is giving your stable. When it is at top condition, it gives the maximum benefits possible. When at lowest condition, it gives the minimum benefits possible, which is only very slightly better than not having the facility at all!
When a Facility is first built it will have a middle level of effectiveness, and will present you with 5 choices about how much money you want to spend each week to develop your Facility. The level of funding that you choose will affect the condition of your Facility each week during the Financial Updates. If you choose the top level of funding, your Facility will gradually improve until it reaches top level (and then be maintained). If you choose the lowest level of funding (no funding) then your Facility condition will gradually deteriorate until eventually it gives only the smallest rewards possible.
Because the change to your Facility condition will only be gradual, you can change this level of funding each week if you need extra money for your stable, and not suffer any major losses. Remember though, the longer you have a lower funding level, the worse condition your facility will become.