Hitting a plateau is when you have seen some results, and then find that the results stall, slowing or stopping altogether.
The reason is generally simple – you have become accustomed to the training plan you are on and need to shake things up a bit.  If you are running 3 miles, 3 times a week, you will need to do something different, or at least increase the intensity in order to keep seeing results. Our bodies are great at becoming efficient – so we need to outsmart it by continually adding new challenges!
If you are training in a gym with resistance, you should never follow the same programme for more than 4-8 weeks (very fit athletes at the lower end of the scale, beginners can go for longer) before you must change at least some elements of the programme, for the same reason. And throughout the programme you need to ensure you are gradually increasing your work as you get fitter – if you are lifting the same weights at the end as at the beginning, or doing the same reps, then you are working out less hard at the end in theory, as should now be fitter! So you need to incrementally increase the work you do – harder variations, heavier weights, more reps etc. When you change programmes you need to change some element of the programme: exercises, rep ranges, frequency can all be altered – and you don’t have to change everything all at once!
Nutrition-wise we often see fat loss plateaus because of calorie creep! You may have got great results at the start, then let the calories or treats creep in as you get more complacent. And ironically, as you lose weight you need fewer calories in order to keep losing – so the lighter you get the harder it becomes in that respect.  However, by increasing lean muscle through resistance training and by increasing your metabolism by using resistance and intervals, you can ensure that your body is in prime condition to burn more calories, even at rest.  But you still need to watch for the ‘treat creep’!
There is a difference between a true plateau and just not seeing results. Either way the important thing is to look at the entire picture: training, lifestyle activity, nutrition, sleep, recovery. If you are not seeing results the answer is ALWAYS in there somewhere, and usually we know exactly where if we are honest with ourselves! Take an honest look at what you are doing, and where you could push a little harder – it is often a case of a simple switch (such as more veggies instead of starches or herbal tea instead of a full fat latte) or taking something you are treating yourself to daily (a cereal bar, a dessert) and ensuring you only allow it once or twice a week.
So the key things:
1. Identify what action you are taking in each of the key areas, and if you have let any one of them slip.
2. Ask yourself honestly what areas you could make changes in (the answers are usually there!)
3. Make a few tweaks and see the results flood back – usually a few tweaks are all that you need!