I've just started playing EVE Online and I've been checking out the forums and I keep on seeing advice for new players that suggest they should 'specialize'. However I really have no idea how to do this. What does it mean?
As you might have noticed already, in EVE Online you won't level up or spec into paths or skills. What people usually refer to is concentrating on some specific aspect in the game or a possible career choice.
For the start, you should concentrate into one race to save time while becoming able to fly more powerful ships. This way you "specialize" into some specific faction and probably at least a basic role as well.
For example, you might want to try Minmatar ships, so you'd start learning skills like Minmatar Frigate (to fly a matching ship hull) and Small Projectile Turrets (to fit matching guns). Once this is done you "specialized" into flying Minmatar Frigates.
What you shouldn't do (i.e. not specializing) would be something like starting to learn Minmatar Frigate as well as Amarr Frigate. While this is something to consider in the long run (especially when you'd like to try pirate faction ships), it's something you shouldn't do at the beginning: You'll be able to board Minmatar frigates as well as Amarr frigates, but you're lacking the skills to fit guns to either ship (i.e. this won't work).
In the end it's up to you where you start, but by concentrating into one area first, you'll be able to get better faster, allowing you to collect more money faster and improving your game experience overall. All factions got their inherent strengths and weaknesses and you're not restricted by your initial choice or race selected: In theory, any character in EVE Online is able to learn each and every skill to the maximum. Only downside: It would take more than 25 years to do so; so you have to pick your favorites.
If you're still unsure, here are some ideas:
TL; DR: To "specialize" here means concentrating on one subset of skills that will advance you and open up new possibilities for you as soon as possible.
If you're still unsure about all this, you should ask on the official forums or join one of the newbie friendly "educational corporations", like EVE University (allows you to experience most aspects of EVE) or Red vs Blue (primarily focused on permanent war and PvP).
I'll go into some detail about specializing on specific ships or shiptypes, mainly for PvP. There are several branches of the skill tree that are only useful if you are flying a specific ship, and don't matter if you fly something else. A rough division of important skills for flying ships would be
In the beginning, choose one race and stick with it for a while. Later you can cross-train.
Pick one weapon system that matches the race you chose and stick with it. Cross-training between turret types is relatively quick, but missiles and turrets have completely separate support skills and training both is something you shouldn't do in the beginning.
This is not a hard rule and there are exceptions to the division along races I mentioned. But in general, choose either Shield or Armor, depending on which race you chose.
Then there are support skills that are always useful, no matter which ship you fly. Those are most of the Mechanics, Electronics and Navigation.
Ship size is also important. If you want to PvP, start with frigates. It takes much less time to train them and they are much cheaper when you lose them. If you want to run missions, train up to at least Battlecruiser to be able to run level 3 missions.
Very simply specializing means training for only a single role or ship. There is a very entertaining 'Whats your persona' tool on the EVE Online website that can be very helpful in starting you off in the right direction.
Once you've run through that there's also this lovely 'what to do' chart.