Could is related to the other modal verb expressing ability, can, but could carries the additional sense of ability under some condition. Can expresses ability, but only in the present tense and in a straightforward way, as in this example: I can come to the party after my guitar lesson. But the examples below illustrate how could ties the sense of ability to a condition.

Examples
If our team had the time, we could make the changes to the document before the deadline.

(This use of could denotes our ability to change the document, under the condition of our having the time do it. Even if the "if"-clause had not been present, could would still have conveyed an implied condition.)

Rick could have bought a larger house if he had saved more money for the down payment.

(Rick's ability to buy the larger house depended on the condition of having more money.)

Could you please send me the revised document before the end of the day?

(This question is asking if the reader is able to send the document. The unspoken condition "if you are able" is implied.)

Would denotes the likelihood of an action or the preference for doing an action, as these examples illustrate.

Examples

I would gladly lend you the money, if I had it.

(The writer is expressing the preference to lend the money, provided the condition of having the money is present, which it isn't.)

I would not wish to be in any meeting in which Ted reveals that cutbacks are on the horizon.

(The writer is expressing the preference to be absent from a meeting, under the condition of Ted's announcement about cutbacks.)

Would you please send me the revised document before the end of the day?

(Unlike the similar sentence with could earlier, this sentence asks if the reader prefers to send the document. In the earlier example, the question was whether the reader was able to send it.)

If those storm clouds were moving east instead of south, it would definitely be raining here right now.

(With the condition of the wind's blowing the clouds in a different direction, the likelihood of rain is greatly increased.)