In simple terms, a letter rogatory is a letter of request from a forum court to a foreign judge, asking for judicial assistance in some form.
This assistance overcomes infringement on the foreign court’s authority and the foreign country’s sovereignty, and is needed when serving process, taking evidence, or enforcing judgments. That definition is where the simplicity ends.
Letters rogatory are normally transmitted via a complicated maze of diplomatic channels. American and Canadian lawyers need the assistance of the State Department and DFAIT, respectively, to convey requests to the foreign ministries of receiving nations. Those counterparts then relay the requests to the appropriate local judicial authority for processing.