Being highly intuitive or psychic means you possess or have accuired one, few or all of the following clearsenses, in my experience, you are born like this, but often we get stifled or block ourselves during our teens, either we get the right support to evolve those special senses or we don't and push them away. Even if you find you have pushed them away, like I have, you can definitely train yourself to slowly recover them. I am so amazed at the human capability for change and recovery.
Clairvoyance - clear seeing
Clairaudience - clear hearing
Clairsentience - clear feeling
Claircognizance - clear knowing
Clairalience - clear smelling
Clairgustance - clear tasting
Usually, you find one or two are more dominant. It is the channel that's more open to you and you may be able to work on the ones that you have trouble with to try and open them more. If you are newly figuring this out, try work with the one that is most dominant and play with it, then go on to another one.
A newer term is empath, an Empath is a highly sensitive and intuitive person.
An Empath can feel your pain as her own, physical or emotional. Empaths often seclude themselves due to the overwhelming feelings that can come over them around other people or in highly energetic places like the city. Empaths attract children and animals, they are also called crystals or indigos in new age terms. Empaths are highly clairsentient.
If you are empathic, it is important for you to learn how to ground, shield and protect yourself, first that may seem like a lot of work, but eventually this happens automatically and you will be able to join the rest of the world without having to seclude yourself everyday.
Understand that nothing can ever truly hurt you and that you need to learn to become an observer of a situation, so you can do the work you need to do as a sensitive, if its a psychic, a healer or teacher.