For any aspiring hacker, it is crucial to understand what hacking is. The media likes to make hacking out to be one of the worst crimes ever known to mankind. While some hacking does justify the negative connotation that comes along with it, most hackers aren't trying to take down the government or get access to Obama's Facebook account. In fact, hacking in itself does not imply malicious intent.
Hacking is a combination of a mindset and a skillset. By far, the most important thing for any hacker is to have the hacking mindset. Hackers manipulate things into doing something that they weren't designed to do. Their mindset allows them to look at something from a different perspective. Think of a bank. A normal person walks into a bank, sees the guard, notices the surveillance cameras and the vault door, and they feel secure. A robber walks into the bank, takes note of the same things and starts to think of ways to circumvent the security measures in place. A hacker is like the robber. They share a security mindset that allows them to look at things differently. The mindset alone isn't going to be enough for someone to rob a bank or gain access to a website, they also need a specific skillset that allows them to know what to look for and what do with what they find. The skillset comes with time, but the mindset is what makes a hacker.
In regards to computer security, hacking is a lot of things. Rooting a server, defacing a website, cracking a hash, decrypting an encryption can all be considered hacking. But the core element is the same: make things do something they weren't intended to do. "White-hat" hackers generally use their skillsets for "good". They do a lot of penetration testing for clients. "Black-hat" hackers are the guys we hear about in the news, they like to hack with malicious intent. Most people fall into the middle category: "Grey-hats". Grey-hat hackers aren't specifically tied to a category. Hacking is their passion and they might bend the rules to fulfill their passion.
TL:DR: Hacking is comprised of the hacking mindset and a skillset tailored toward their area of interest. The mindset is the key component of any hacker's toolbox.
If you haven't already, check out the "How to Hack" article here for some more information on how to get started with a life in hacking.