Ability is the skill or competency(能力项) to perform a task whether it is physical(身体的) or mental(精神上的). An ability is something that is inherent(继承的) upon the genetic(基因的).

Ability是指与生俱来的生存能力。

Example:

Bird has the ability to fly.

鸟天生就有飞翔的能力。

Capability means the ability to perform specific actions or achieve specific outcomes. Particularly in business it describes what an organization does. People care whether they know how to do it.

Capability指的是完成某特定需求的能力。

Example:Jack has the potential capability to finish 1000 meters race to 2.5 minutes through training.

通过训练，Jack有潜力在2.5分钟内跑完1000米。

Capacity describes the quantity of something. People cares if it is enough to achieve and complete something.

Having the capacity to deliver(交付) goods and services is more important than just having the capability.

Capacity是人们在指定的时间内能够完成的最大工作量。侧重结果，并且这个结果通常需要多方资源协调才能实现。

Example:

The capacity prediction in the next quarter is 110%, we must pay attention on it.

下个季度的生产能力预测是110%的量，因此我们必须要留意。

Competence describes the quality or state of having sufficient knowledge, strength or skill to do something well enough. Competence is another word to describe skill.

Competence指的是一个人具备的能力项。这个能力项是可以后天训练培养的。比如团队合作精神、责任感、商业意识、决策制定、沟通交流能力等。

Example:

Teamwork is one key competence for the majority of careers.

对于大多数职业来说，团队合作精神都是一个员工的关键能力项。