For a long time, it has been common knowledge that people should lift 1-5 reps for strength, 8-12 reps for muscle size increase, and 15-20 reps for muscular endurance. However, more recent research has demonstrated that almost every rep range stimulates the same amount of muscle growth so long as effort per set (i.e. closeness to failure) is the same between sets. In other words, a set of 50 reps taken to failure stimulates the same amount of muscle growth as a set of 5 reps taken to failure. Currently, evidence exists for loads as low as 20% of 1 repetition maximum and as high as 90% 1RM stimulating the same muscle growth, so long as effort per set and number of sets are similar. Performance-wise, you will improve the most in the rep ranges that you practice. If you mostly lift with 1-5 reps, you will mostly improve performance in the 1-5 rep range. If you mostly lift with 15-20 reps, you will mostly improve performance in that rep range. This is likely due to neural adaptations rather than differences in muscle growth; you are “studying” that specific rep range, so your nervous system learns to perform it the best.
There are other advantages and disadvantages to different rep ranges besides performance differences even though muscle growth is the same between them. Heavier loads stimulate more bone and connective tissue growth, and lighter loads have less risk of injury and may have increased cardiovascular benefits. However, the main thing is to lift in a way that you enjoy and that encourages you to put forth high effort.
There is also a common misconception (which somehow refuses to die) that certain rep ranges (usually stated as 8-12) are for “burning fat” or “toning” and if you have those goals, you should stay away from others (usually stated as 3-5), which are for “bulking”. This is not based on anything real. Besides the fact that body parts cannot be “toned” to begin with, achieving fat loss is a product of calorie balance and has absolutely nothing to do with rep ranges. If you want to trim fat from your body, look to your diet.