When I see a request to fill the "Initials of First Name(s)" on registration, what does it mean? Does it mean that I have to put the first letter of my first name or it means something else?
An initial is the first letter of a given name, therefore yes, you are correct in your assumption that you have to put the first letter of your first name.
The reason that the form allows for a possible plural in Name(s) is that in many cultures, people can have more than one first name (the actress Sarah Michelle Gellar for example), therefore the person may choose to use more than one initial.
Put in the first letter of your first name. I would guess that the plural is so that, should you have multiple first names, you can put both initials in (e.g. "Mary Jane" -> "MJ", although I would expect people to just use M).