If you are keen to improve your skills in golf or tennis (for example), then sports specific training could well be the answer.
There are various reasons why people work with a personal trainer but one common reason is people who want sports specific workouts. Almost any activity, performed at a reasonable level, will benefit from sports specific training plans. Tennis, rugby, golf, running a marathon or taking part in a triathlon - in each case your performance will benefit from sports specific exercises.
A trained and qualified professional is likely to have certain activities in which they are something of an expert. Many times these will be events in which they themselves have participated, or indeed in which they continue to participate, often at quite a high-level. If this is the case, you may reap the benefit of a high-level of expertise and experience. While almost any reasonable workouts will improve performance in your chosen activity, the huge variables between various events mean that tailoring your workouts can be tremendously important.
When you work out, there are a range of areas that you have the potential to improve - your strength, stamina, flexibility, agility, and speed, to name but a few. Different workouts will be appropriate for each, in different proportions. For example, if flexibility is important to you, then Yoga would be an option, while football players, who need to be able to perform repeated bursts of speed, often take circuit classes.
Finding the balance between all the areas is the trick, and that is where the services of a good personal trainer can be invaluable. They can design a series of workouts ideal for the activities you have in mind, and monitor and adjust the as your fitness improves.