You kind of answered the question yourself:

A map can contain any type as long as all the elements are of the same type

So, with this, what does map(object) mean? It means it is a map, where the type of all of the values in the map must be on object. This is most useful when you further define the types of those objects. For example:

variable "allowed_security_groups" {
  type = map(object({
    id = string
  }))
}

This is a map where every value must be an object with an attribute id. This sort of type definition can be very useful for modules that need to iterate over something with complex inputs.

resource "aws_vpc_security_group_ingress_rule" "allowed_security_groups" {
  for_each = var.allowed_security_groups
  security_group_id            = aws_security_group.this.id
  # The type declaration guarantees that every iteratee has an id attribute
  referenced_security_group_id = each.value.id

  from_port = 443
  to_port   = 443
}