A fitness trainer (also known as a personal trainer) is a professionally qualified person that is able to work with you to develop and guide you through a training program to realise one or more health related goals.
You don't need a fully equipped gym to work out. All you really need is an exercise mat, a decent pair of trainers and maybe a skipping rope and some weights (for strength training). Lots of fitness trainers are able to travel to your home for private training sessions or you can arrange to meet them in a local park.
A major benefit with using a private fitness trainer is that they will be able to develop an individually tailored program for you and will provide far more one-on-one guidance than is possible in a group setting.