If you want to build powerful and big arms, building a big triceps is most important. Triceps size is more important that size of your biceps because triceps make about 2/3 of arms size. Also, having a strong triceps is also very important for many compound movements for bigger muscle groups like Bench Press and Military Press.
Triceps isn't one muscle, it is three-headed muscle and it is composed of three heads - long, medial, and lateral. To build bigger triceps you need to perform a workout that targets all three heads for bigger and stronger triceps. An ideal rep range for muscle hypertrophy is 8 - 12 and as your triceps becoming bigger and stronger you should put heavier weights to activate your triceps to grow more.
Tip: If you triceps is lagging behind other muscles then you should work more on training your triceps and separate it from classic Chest/Triceps workout, or start a workout with triceps exercises first. It is right that chest exercises also hits triceps but this is only if your triceps is really your weak point and you need to build it faster for better body proportion.
Which exercises to perform for bigger triceps:
1. Narrow Grip Bench Press
This is the ultimate exercises to build triceps size and strength. Performing close grip bench press allows you to lift more weight which results in faster muscle and strength gains. Remember to keep elbows close to your body and hold the bar at the middle, no further than shoulders width.
2. Dips
Dips are also great for building bigger triceps and they hit all three triceps heads. You can do weighted dips by sitting on one bench while putting your heels on other bench and weights in your lap. If you are a begginer in a gym then just do regular dips, they are great for starters to build their triceps size, and when you get stronger start adding weights or wear weighted bell. Apart from bench dip, tradiotional dip is also a great exercise for triceps building.
3. Skull Crusher
Skull crushers mostly work the long and medial head of triceps and it is a very good exercise for building massive triceps. Lay down on a bench and hold a EZ-bar and keep your elbows tight as possible to better activate the triceps.
4. One-Arm Triceps Extension
Overhead triceps extension with dumbbell mostly target lateral head of the triceps. Training lateral triceps head is very important for building well-shaped and big triceps.
5. Triceps Rope Pushdown
This is a machine exercise and that is why I would leave it for a last exercise of triceps workout routine. It is very important to keep your upper arms locked at your sides and your back straigth while performing rope pushdown exercise.
6. Diamond Push Up
Diamond or Triangle Push Up is very good exercise for triceps development. I personally like to perform this bodyweight exercise after these first 5 exercise from the list. It can be a great finish for triceps building. Diamond Push Ups is the best bodyweight exercise after Dips when it comes to building bigger triceps and it is great for beginners. If you do first 5 exercise you can add Diamond Push Ups for more triceps pump and perform only two sets of how many reps you are available to do after all these 5 exercises.