To dream that you are swimming suggests that you are exploring aspects of your subconscious mind and emotions. The dream may be a sign that you are seeking some sort of emotional support. It is a common dream image for people going through therapy.
To dream that you are swimming underwater suggests that you are completely submerged in your own feelings. You are forcing yourself to deal with your subconscious emotions.
To dream that you are swimming away from someone or something indicates that you are avoiding some deep emotional issue. You are refusing to acknowledge and confront your feelings because it may be too painful or too fresh. In particular, if you are swimming away to escape danger or death, then it suggests that you are letting fear take over your actions. You are afraid of change.
To see children swimming in your dream indicates that you need to adapt a more carefree attitude.