'Could' is the past tense of the modal verb 'can'.
'Could' like its present tense 'can' should ordinarily express 'ability'
'Could' acquired a slightly distant meaning, over decades and centuries of use.
Usage of 'Could' in making polite requests:
'Could I speak to Mr.....?'
This is said to be a politer form than--
'Can I speak to Mr.....'.
How? It is not clear. Usage, probably justifies the 'politeness'.
Another funny thing is : 'Could' is a verb of past tense. How it is being used in a request which refers to a future action which depends on granting of permission by the other person?
'Could' represents ability, isn't it? Let us now see, how it gained a meaning of 'having ability, but not doing it' .
We could come out of the emergency exit, when the coach caught fire. (This according to interpreters, means: We had the ability to come out of the emergency window, but we did not use that ability.)
They suggest the following alternatives:
1. We 'were able to come' out of the emergency window ....etc.
2. We 'managed to come' out of the emergency window ...etc.
The interpreters are willing to accept the negative usage:
We 'could not' come out of the emergency window. Its latch was too rigid to open.
Some interpreters consider 'could' as less positive than 'can' and 'may'
I could attend the wedding. (This is said to be less positive than 'I can attend the wedding'.)
'Could attend' should actually refer to a thing of past. But, it is not clear how some speakers are using it to refer to future ability/possibility/probability.
'One observation on the development of usage of 'could' to seek permission or grant permission
The Manager nodded his head and said to the employee: "You can go."
The Manager nodded his head and told the employee that he could go.
We can deduce an interpretation here: The employee was earlier not enabled to go. He is now enabled by the Manager, to go. We can also justify the use of past tense 'could' here, because the verb in the reported clause is to be in line with the reporting verb 'told'.
Another example of negative connotation of 'could'
He 'could have accepted ' the job.
We get here, a negative implication that he has not accepted the job.