Strong adult attachments give a child a fundamental sense of security. It allows them to be vulnerable, adaptable and curious without fear of ridicule or loss, which in turn gives them trust and confidence. These two qualities allow them to develop a strong sense of who they are and to develop their potential much earlier than those who do not have those qualities.
The primary adults in their life taking a strong lead rather than looking to the child for guidance also allows the child to get on with the business of maturing emotionally and developing a strong sense of self. Without these attachments and someone to look to as a compass point, children will be much more easily led (or on the flip side become alpha agressive bullies leading others), and also do not have confidence and skills from which to develop a strong sense of identity. Curiosity, teachability, and confidence all require the ability to be vulnerable and to trust.
The reason that adult attachments are more effective than primarily peer attachments is that peers are in competition with their friends and are immature themselves, so those relationships are often much more wounding and require the constant frustration (and ensuing agressions) which results in needing perpetual proximity to prevent someone else taking one's place. Therefore they have to harden up and not be as vulnerable. They look to less vulnerable ways of attaching to others (usually peers), primarily by trying to be the same as them. The problem with doing that is that you cannot be part of a group without losing a sense of self, until you have become a viable, separate individual, which most children have not yet become.
By creating a village of adults who can cheer a child on, mirror a positive image of themselves back to them, teach them new skills, get them comfortable in a variety of situations, walk them through new experiences and be there for them emotionally, and offer a context for peer friendships, a child is going to emerge much more emotionally mature at a younger age and with a better sense of who they are.
Parents often feel that by the time their children are teenagers they need to let go completely. If things are as they should be, there should be a sense of friendship (with the parent as the leader) throughout the years leading up to becoming a teen. This requires spending time with the child, getting to know them inside out, having lots of discussion (which means time together needs to be ample, as those discussions don't happen all the time), and the parent needs to be willing to listen to a lot of "drivel" before getting to the important things.
Throughout all the growing up years, the parent is still in charge, but takes into account their child's wishes, needs and points of view as they make those decisions. They are their child's best bet - their provider, their comforter, protecter, their biggest fan. As a child becomes a teenager, this doesn't need to change. If the relationship has been in place as it ought to be, the child still looks to their parent as their compass point, wants to tell them their heart, discusses decisions with them. I think there is a security in knowing where the lines are and yet feeling like it is possible to know why they are drawn there and to feel that the person in charge cares most for your happiness and well-being of anyone in the world and is worthy of that trust.
I think the other factors for developing a strong sense of self are exposure to many different types of experiences, getting to know a wide variety of people (ethnicities, cultures, cross-generation, related and non-related, professions, skills) and being given the proximity to be able to learn from them and have time with them. Looking for strengths of the child from the time they are little and building on those is tremendously helpful, as well as shoring up areas that look like they may be potential weaknesses. Mirroring back what qualities you see in your child is very affirming and gives them a better picture of who they are. Chances for a lot of discussion allows them to learn about the world the around them and also have a safe sounding board for different opinions and points of view that they would like to try out. All of these contribute towards making a child self-assured and well-prepared for life.