Split training refers to working out different parts of your body at each session, instead of training your entire body at every workout. For example, you can work out your upper body one day and your lower body another day. Some splits break the body down further. If you work your back muscles separately from your chest muscles, standard fitness guidelines recommend training your biceps with your back, but this recommendation isn't set in stone.
The push/pull split is a typical upper body workout split. You train your biceps with your back and your triceps with your chest. The reason for this split is because your biceps are involved in most compound back exercises and your triceps are involved in most compound chest exercises. When you perform pullups, pulldowns or rows, your biceps are secondary movers. When you perform chest presses and pushups, your triceps are secondary movers.
If you train your biceps separately from your back muscles, you may overtrain them, because you will work them twice — once on back day and then again on biceps training day. Even if you are not focusing on your biceps, they are involved during many back exercises. If you train your back on Tuesday and train your biceps on Wednesday, you are essentially working your biceps two days in a row. Your muscles recover and grow when they are at rest, not when you are training them.
Not providing enough recovery time between workouts can cause your muscles to atrophy, or become weaker and smaller. Weight training causes microscopic tears in the muscles, which is considered to be the likely reason why you experience muscle soreness after a workout. The muscle needs time to repair itself and prepare for the next workout. The American Council on Exercise recommends resting large muscles at least 72 hours and smaller muscles at least 48 hours after a workout.
Strength training and working out have very few hard and fast rules. You can train your triceps with your back, but if you do, you need to add in extra rest time for your biceps so you don't train them too closely together. If you train your back and triceps on Monday, you could train your chest and biceps on Thursday. This gives your muscles 72 hours of rest. Schedule a leg day between the upper-body workouts.