Could has two slightly distinct uses. One is the past tense of the modal can, indicating possibility/permission/capability in the past:
I could have married someone else, you know.
The other is used in the present and future to indicate a hypothetical, a possibility not simply about possibility/permission/capability, though that can be an element.
I could punch you in the face.
This means that I have the ability to punch you in the face, and that I'm raising the possibility that I might take that action - it's a hypothetical
It could rain tomorrow.
This not only indicates possibility, which is after all always there for most of the world's population, but it is specifically pointing it out as a hypothetical, that might be used in a conversation to prompt other people to think about what might be done in that situation.
Using I could when making an offer to someone is usually about recognising that you aren't giving them all they wanted, but are giving them something that you think might do.
"Do you serve babyfood?"
"No, but I could warm up some that you have with you."
It's also used for threats, raising possibilities in relation to future plans, and so on. Some consider it an example of how English forms a subjunctive, which many other languages have as a distinct mood with distinct verb forms.