That depends on the type of visa you require. There are usually two types: business or visit.
For the business visa applicant, we require letters from your UK employer and the company you are visiting in Ireland confirming that a multi entry visa is required, the reason why and the period during which the repeat visits will take place (see the business visa checklist on the "Supporting Documents Required" page).
For the visit visa applicant, you need to show that you have a good Irish visa history before we will consider issuing a multi entry visa. This means that you need to have had at least two previous Irish visas in recent years, no adverse Irish visa history (i.e. previously entering the country without a visa etc) and have abided by the conditions of the previous visas. You also need to explain to us why you need a multi entry visa.