1. Transportation to and from Roatan will be busier. The ferry normally doesn't run on Good Friday (this year, that's April 3rd), and the rest of the week will be very, very busy. The hours that it runs will probably change so that a 3rd ferry can be offered, and you'll probably need to get there a couple hours ahead of time to get tickets. Domestic flights will also be busier.
2. Places to stay will be busier. This is definitely a time of the year that it's good to reserve ahead of time (one year, we had someone pay to sleep in a hammock!). Most places have a minimum number of nights you need to stay.
3. There will be businesses that are shut. Banks normally shut by mid-day Wed. ATMS will be available, and the bank at the airport needs to be open as people have to pay departure taxes. Schools are off for the week, most government offices are closed for the week too.
4. Holy week isn't very holy in Roatan. There's not special religious or cultural events, it's more like a week-long party (think Spring Break Florida or Cancun and you'll get the picture). There is a lot of drinking and partying for these dates: police will be more vigilant, looking for drunk drivers, so if you're renting a vehicle, be prepared for traffic stops (make sure you've got your license and know where the vehicle registration papers are). West Bay beach gets very, very crowded.
5. If you hate crowds, there are still places that you can escape to. It's a bit harder than normal (even Camp Bay is full of people!), but it's possible. The backyard of the hostel by the pool is actually usually quiet all week, even though the hostel's full, as most guests are out joining the rest of the crowds.