“One should be able to move in any direction with ease. When attacked the natural reaction is to go back. You should practice hard to overcome this.” – Hironori Otsuka 10th Dan Wado-Ryu (1892 – 1982)
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In actual combat the objective is to escape, or if necessary, to control, or to hit and not get hit. While some develop a defensive system which relies heavily on pressure and power, others base their defense on lateral movement, precision, and fighting smart. Developing a sense of the variety of ways to hit and not get hit.
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Practitioners who know the importance of angles know the significance of every movement and how they can use it to gain an edge over an opponent. Moving to an angle is a key principle in karate. But in many forms of competition, training is often performed in linear movement with speed and strength. And while this may be okay for competition, for actual self-protection it may not.
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We can see that attacking an opponent from an angle is more beneficial than attacking head-on.
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Angles in kata, and any technique within that ‘template’, are very important to give you an advantage. To help us with this, the embusen within a kata, tells us the angle to which you must take relative to the opponent for the technique to work at its optimum.
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The kata tells us, ‘do whatever you need to get to this angle’, and then you’re in the optimum position for this technique to work successfully. Don’t be deceived into thinking the embusen is the line that the enemy is attacking from. The embusen does not represent turning to face an opponent. An Attacker should be in front of you … but you should NOT be in front of him. The angle represents the position you take relative to him.
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Getting to these angles has all kinds of advantages; i.e. we can strike directly and efficiently, whereas the enemy’s possibilities to attack are reduced. Additionally, we can also gain a mechanical advantage, an advantage with leverage, or to facilitate unbalancing. The enemy’s limb is directly in front of us, with the attackers other limb is further away from us and / or checked.
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Do whatever you need to get to an angle, and then you will be in the optimum position to perform your techniques efficiently and with precision, and you will be able to control the enemy’s line of attack. If your techniques are to be realistically implemented in actual combat, either in defense or attack, the learning and understanding of angles in karate is a basic critical skill. 
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