There are many training techniques that will enhance the effectiveness of a strength training workout. Simply lifting an arbitrary amount of weight for a preset number of reps will usually generate results at the beginning of a program but fail to lead to significant hypertrophy - when muscles get larger. In men, muscles often do actually grow larger. In women, hypertrophy usually takes more the form of muscle "definition".
One extremely effective training strategy is called "fatigue plus one". This means that you lift a certain amount of weight - the amount that will generate a maximum of 10 reps and no more - and squeeze out one last rep. This "plus one" is psychological, because your body will feel like there is nothing left. We know from recent research that the limiting factor when it comes to exercise fatigue is the brain - when our bodies feel like there is no more energy, this is actually untrue. It is the brain that sends the message that nothing is left. This does not mean that you can do an entire other set when you have worked to failure. It means that you can override your body's sensation of complete fatigue, dig deep, and squeeze out one more. Two important things to note: this type of training is very hard and not for everyone, particularly individuals who have musculoskeletal issues; and a rule called "technical limit" must be adhered to, meaning the first and last rep must look exactly the same. A sloppy "plus one" will lead to injury, or at the very least not produce the desired training effect.