In EVE Online, every character has implant slots in his or her head. Implants can be purchased on the market in EVE Online (or acquired in other ways) and then plugged into your character's head. However, when you remove an implant, it is destroyed (much like a ship rig). Similarly, if your character gets podkilled, all of your implants will be destroyed.
Implants can't be manufactured, so your only ways to get them are:
Because of how limited they are, implants are very expensive on the market. It's cheaper to get implants from NPC Loyalty Stores (where you can buy implants for some loyalty points and some ISK), although you will have to of course build up loyalty points with that corporation to benefit from the lower ISK cost of the implants there.
Occasionally, storyline agents will give you implants. If you have been working with a high-level agent of the corporation before getting a storyline mission, then you're more likely to get a higher-level storyline agent who will give you a higher-level implant reward. Even if you don't get as good an implant as you want from the storyline agent, remember that you can sell the implant for a huge sum on the market, then use that ISK to buy from the Loyalty Store of your choice.
Train up your Cybernetics skill to at least level 1, then right-click on an implant that you have the requisite skills for (check the information window), and choose to install the implant. It will be in effect immediately. If you remove the implant, it is destroyed (but your character is unharmed).
To have ten implants installed at a time, train Cybernetics to level 5.
There are two types of implants. One type is the skill hardwiring implant. A skill hardwiring implant will improve an attribute that can normally only be improved through skill training. For example, there are implants that increase armor HP in the ships you pilot, as well as implants that improve targeting range, implants that reduce cycle time for salvage modules, and so on.
The other type is the attribute enhancer. This type simply increases one of your character's attributes, which speeds up skill training time. The best attribute enhancer implants increase an attribute by five points. There aren't any implants to increase attributes by more than five points.
If you get podkilled, your implants are destroyed. If you have jump clones, each jump clone has its own set of implants. If you jump from a clone that has implants, you will not be able to use the implants in that clone until you jump back to it.