So, there are two types of belly fat: Visceral (sit around your organs) and subcutaneous (sits under the skin but usually over the muscles). When you work out, especially your abs/core, your abdominal muscles start to tighten and become more firm. If you have a lot of subcutaneous fat, it may seem to become softer as your abs become tighter and less supportive of the fat. But in reality, it's just as soft as it always was except your muscles have basically shrunk away from the surface of your skin.
If you continue to work out and do more aerobic exercises that burn fat, the subcutaneous fat will start to melt away and your belly become tighter if you follow @tonynyc 's advice and burn more calories than you take in. Your body will start to use your body fat to create energy for you. I know it can be discouraging at first but you are on the right track as far and shrinking your belly (if that is your desire). Just keep at it. As the fat melts away, your abs will become more defied over time. Good Luck!!