The Trainer Fitness Plan is a Fitbit Premium feature that sets a 12-week goal for you based on your historical data. You can ask your Trainer to either maintain or increase your activity levels.
Weekly goals cannot be manually adjusted, but if the Trainer determines that the goal is too easy or too hard for you to achieve, the option to edit your goal will be available once you have completed a week. That's all it does; and while it may not seem like much, to me it's one of the best features in the Premium package, and the one reason I will likely renew my Premium membership. The 12-week plan increases the demand in small weekly increments; such that for a given week, you barely notice the additional effort required to meet your goal. But over the 12-week time span, those small weekly increments do make a big difference.
As for adjusting the amount of food you can eat during the day, your One already does that. When you set up your profile settings, Fitbit.com pegged your BMR. As you log your food and activities during the day, everything gets adjusted. The Trainer functionality in the Premium subscription just adds one more tool to your kit by creating an additional incentive to improve your activity level, over a 12-week plan.