Capability is a certain ability, the quality of being capable, a potential aptitude. Capacity is the ability to contain, that is: volume or amount that fits in a certain container for example. The maximum amount that something can contain. It is also a certain rank: He/she was employed in the capacity of merchandising designer. There are also other meanings, some are legal jargon, like "the Parliament´s capacity to create new laws", that means, legal competence exerted by a certain person or institution.

Capability could be described as "potential ability". Capacity can be used in the same context but the feeling is a little broader. Here are some examples... "He has the capability to be very good at the guitar." "He has the capacity to understand Einstein's Theory of Relativity." Capacity can also refer to volume and physical abilities as in... "This truck has the capacity to tow a three-ton vehicle." "This jug has the capacity to hold one and a half gallons." Hope that helps!