When there is chronic muscle tension or injury, there are usually adhesions (bands of painful, rigid tissue) in muscles, tendons, and ligaments.
Adhesions can block circulation and cause pain, limited movement, and inflammation.
Muscles must be relaxed in order for the therapist to reach the deeper musculature.
It shouldn't hurt, but it's likely to be a bit more uncomfortable than a classic Swedish massage. You should always feel free to speak up if the pressure is too much for you.
It's important to drink a lot of water after a deep tissue massage to help flush lactic acid out of the tissues.
If you don't, you might be sore the next day.
It's possible that you might feel some soreness the day after a deep tissue massage even if you DO drink water. This just means a lot of waste products were flushed out of the tissues. It should pass within a day or so.