Your character can be enhanced in a lot of ways and his/her growth will depend on your playstyle, perk assignment, and equipment. Consider the following tips to shape your ideal avatar in the post-apocalyptic wasteland.
Watch the SPECIAL video tutorial during game installation
When you first load your disc in your console, the system will install local cache data of the game for better performance. While waiting, the tutorial video about the SPECIAL attributes in the game will be played. These play a key role in your character's overall development. If you missed these videos, you can find them off Bethesda's site.
Avoid maxing out your attributes from the get-go
When you get the chance to modify your stats, you'll be given 21 points to spend in the initial development of your character. As you gain experience and level up, you can gain 1 Perk point to spend either by learning a new perk or adding it to your SPECIAL attribute. Take note that you can find Bobbleheads and Magazines that permanently increase your stats and perk levels so maxing out an attribute early on is not really recommended since you could've distributed some of those points to your other attributes.
Decide on your character's "build"
Randomly selecting perks and SPECIAL attributes will get you nowhere, even if its possible to max out the perks later in the game. Select the perks you want on your type of gameplay. If you're into melee Combat, build a character with high Strength, high Endurance and supporting perks like Toughness, Iron Fist, Big Leagues, Rooted, Etc. If you want to build a stealthy character, consider having a character with high Agility and considerable Luck with supporting perks like Sneak, Ninja, Moving Target, Quick Hands, Blitz, Gun Blitz, and more.
No more Karma System
Previous Fallout games have the Karma system which provides players a variety of options and flexibility to make their own approach in a given situation or quest. Sometimes this includes the option to help the "bad" guys, betray the quest giver, or take advantage of a situation at the expense of other characters. This system doesn't seem to be prevalent in Fallout 4 so playing as an evil character won't have that much merit compared to when you're playing as the generic hero or neutral character.
Companions and Romance
Later in the game, you'll encounter key characters that will join you in your adventure and who you can even romance. However these "relationships" have no much depth so don't expect anything long term or settling down. Companions are very useful NPCs that will also provide you with bonus perks in addition an extra hand in Combat and hauling loot.