It's hard to explain, so I'll put it this way.
Assuming you know what a Bench Press is, when you push up there is positive resistance. Say the bar ways 45 lbs and you have 55 lbs of weight plates then there is 100 lbs of positive resistance. When you let the bar down after you have pushed it up there is 100 lbs of negative resistance, because it is coming towards you, you are not working to push it up but rather to take it down.
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Resistance is essentially the amount of weight you are lifting during a resistance/weight training workout. Higher-resistance routines will involve more weight and usually fewer repetitions, while lighter resistance workouts involve less weight with more reps. Working with higher resistance levels (more weight) will build more strength and size, while working with lower resistance and more repetitions (15 or so plus) will result in more muscular endurance and definition.