When most people this of fitness they think of someone who can run a long way: "Our Martins pretty fit mind, he just ran a 10k" "Whys he got a beer gut though?......"
I believe fitness is a mixture of many disciplines, sure many people will excel in one aspect more than others, but to be truly fit... You need to be able to do more than run for a long period of time.
There are no set guidelines for what fitness is, and many of the worlds largest fitness organisations wont clearly set out their guidelines for what fitness is (Probably to avoid alienating various sections of the fitness community) I personally see fitness as a well rounded mixture of: Strength Cardiovascular fitness, Flexibility Speed Endurance Power Motor Skills (E.G Reactions, Timing, Coordination etc)
Can you truly be classed as a fit person if you can Run a half marathon but can touch your toes? Can you be classed as a fit person if you can bench press 120kgs but you cant run 5k? Are you a fit person if you can cycle swim and run long distances, but if someone throws you a ball to catch you fumble it onto the floor.
Everyone has a preferred way of exercising, a way that they just enjoy! A form of exercise that they look forward to and really gets the best out of them, But sometimes its the things we like to do least that we need the most.
To be truly fit I believe your exercise program needs to cover all of the above in detail, sure there will be a focus on a few more than the others depending on what your training for, but every program needs to have a well rounded selection of all of the above and I believe there is no one better placed to do that than a personal trainer, because lets face it, on the days when your workout contains the things you don't like doing (but you need) the accountability of a personal trainer as well as the motivation program structure and exercise selection that he/she will bring is priceless, and the difference between reaching your goals.... and constantly chasing them.
Personal training does not offer "one size fits all" Programs, clients are assessed individual and have personal programs devised that phase in and out of the different key components of fitness so that our clients are as fit as they could be. Experienced personal training clients know that they could run a 5k at a good pace, Lift their body weight or more in various resistance exercises, demonstrate good flexibility, have quick speed and fast reactions and when you have all of that at your disposal... Its impossible not to lose weight, tone up and look as fit as you are.