Its called a running martingale. You can look it up to get the idea of what it looks like, but it attaches to the girth and goes around the horse's neck and two rings come off of it and the reins go through, so if the horse lifts his head up he feels more pressure on the bit pulling his head down. I am not a huge fan, but I would talk to your trainer more about it, maybe she can offer you reasons why a running martingale would be useful in your particular situation.
Yes, we were all new to this at one point in our lives and no question is a dumb question.
Fanfara, my advice would be for you to ask your trainer why he/she recommends a running martingale for your horse.
My horse wears one for jumping as he tends to lift his head so high he can knock your teeth out with his head! But seriously, it helps control him because he can't evade the bit by tossing his head way up.
"Another member of the Barefoot Eventers Clique"
If adjusted correctly, a running martingale should not have any effect until you NEED it -- ie, when the horse throws his head around or raises it to a dangerous level. I remember Jimmy Wofford saying that the middle of a course is a bad place to find you need a martingale.
On the other hand, if you need one for ALL work, including the flat, in order to bring the horse's head down "in a frame," you're not using it correctly and have other issues to address.
That said, I'm pretty sure there's a reason you are paying your trainer money, so why not ask them about the purpose and function of the gear that they are recommending?