This would probably be better suited for English, as it's a phrase that really has nothing to do specifically with aviation. However...
dotted your "I"s and crossed your "T's means that you've paid attention to all the details, that you've finished everything that needs to be done, the job is complete.
An uncrossed "T" could be a capital "I" or a lower-case "L". An undotted "I" could be a lower-case "R" or "E". These are especially true of hand-written, cursive letters. So crossing your "T" ensures clarity and completes the job.
When the dispatcher said this to the captain, he was telling him that he'd gone over all the details and the job was done.