Could is the past tense of can. It is used to talk about ability that existed in the past.

• In my younger days I could run four miles at a stretch.
• Till last year, I could read without glasses.

Notes:
Could refers to past time only when the context makes it clear.

Could is the past tense of can in indirect speech.

• Direct: She said, ‘I can’t lift this box.’
• Indirect: She said that she could not lift that box.

Could is used to talk about possibility or uncertainty in if-sentences.

• You could do it, if you tried hard. (Possibility)
• We could succeed, if we all pulled together. (Possibility)

Could is also used to ask polite questions.

• Could I have a word with you?
• Could you take me to the Vice-Chancellor?

Related posts:

1. Modal Auxiliary Verb Would
2. Uses of Would
3. Uses of Should
4. Modal auxiliary verb shall
5. Can and May