It's an abbreviation of 'I would' and sometimes 'I had'.

I'd = I would or I had - NOT I could This is what we call a contraction - when two words are contracted into one, these are nearly always used in spoken English and in informal letters or emails. Example : She'd come. if she was invited = she would come.....(second conditional) A2 pre-intermediate If he'd gone to the party, he'd have enjoyed himself = If he had gone to the party, he would have.......(third conditional) level B1 intermediate I'd like to dance = I would like to dance. (something I want to do now or in the future) level A1 elementary.