Could

It means (Past form of Can)

I) It Express Past ability:-

1. My grand father could eat four plates of birayani when he was young.
2. Before his eye operation he could not see clearly.
3.  He could run 5 Kms till last year.
4. He could walk fast before he met with an accident last month.
5. I was very busy so I could not prepare for the seminar. 

II) To seek permission in a polity way or request:-

1. Could I leave early today?
2. Could I make a call from you mobile?
3. Could we come late tomorrow?
4. Could I take your bike for a while?
5. Could I say something?
6. Could you give me two days leave?
7. Could you give me a glass of water?
8. Could you switch off the fan please?
9. Could you please reserve a table for 4 people for tomorrow evening?
10. Could you please tell when is the next train?
11. Could you please show me how to solve this problem?
12. Could you please tell me how to open a new account?

III) In indirect reported speech could is used as the past form of can:

Direct Speech : Pavan said to varun” I can run fast.

Indirect Speech: Pavan told varun that” he could run fast.