The main components of physical conditioning are aerobic, anaerobic,
strength, flexibility, explosiveness, agility and speed.  Aerobic
training involves the endurance component.  It's the base of your
conditioning.  Aerobic training involves longer, more steady state
activities.  Aerobic training also utilizes oxygen to produce energy. 
For example, a 20-minute run will help you "cruise" up and down the
field.  Anaerobic training refers to shorter, more explosive activity
like a 20-yard burst to get by defenders.  Anaerobic is shorter in
duration and more intense.  Anaerobic also occurs with insufficient
oxygen to the muscles.
The game of soccer is a balance between sprinting, cruising, jogging,
walking and recovering.  Soccer fitness is about your ability to
recover quickly from performing an activity, and then being able to do
it again.  You must start with a foundation.  The deeper the
foundation, the greater the structure you can build on it.  You can't
start out running four miles if you haven't done anything in a few
months.  It's a process.  Performing too much work before you are ready
will result in injury.  Also, do not expect to get fit overnight. 
Fitness will come over time and will be dependent on the program and
how much time you put into it.  For more specific details as far as
fitness programs or testing, feel free to ask.