I started to answer but decided it might be easier to just do a search and see if another site already had a good answer. I found a pretty good one:
Here is part of their page titled What is an Empath?
An empath is someone who picks up on the emotions and / or feelings around them. It may be the feelings of someone they are close to. It might be the general feelings in a room or even when there is a very strong emotion around the world, such as fear.
I believe that we are all empaths at some level, but it seems the majority are so low level that they aren't aware of any other feelings but their own. They might be considered the lucky ones.
The ones who are prone to problems are what I call high level empaths. They are like a psychic sponge, picking up feelings and emotions from all around them. Most of the time, they don't even know they are doing this, and do not understand that the feelings they feel are not always their own ones.
For instance, you might be feeling good, but suddenly, for no apparent reason, you have a drop in your emotions. This might be due to a friend or partner dropping in their emotions and you are picking up on this. This is a sympathetic attachment, and it's not unusual for someone to feel down or depressed in sympathy with another. Unfortunately, it's not healthy, either.
Most high level empaths who pick up feelings like a sponge, tend to do so because they are ungrounded. This means, part of them does not want to actually be here on this planet, and so the spirit is 'out there' rather than in the body. This becomes a viscous cycle, as the more ungrounded you are, the more negativity you can pick up, and the less you wish to return to your body.
Grounded people are rarely swayed by another's feelings, even if they do feel them.
Empaths often suffer greatly because they do not understand what is happening to them. They are not aware that their feelings are not their own. They do not understand why they are feelings depressed, anxious, desponded, etc, and rarely will they actually connect it to others.
Most high level empaths are prone to clinical depression and are prone to take on the problems and pain of others, as though that will lessen it.
Being an empath doesn't have to be all bad, though. It can be a very powerful and potent tool for connecting with others and helping them to heal. It can also bring an incredible amount of joy if you are able to control it.