For me it means to keep yourself pure physically and mentally. It is truly a challenge based on how the world is.
For me, it means not having sexual intercourse except with your spouse to whom you are legally and lawfully wedded. But I also think it goes further than that. The Lord also taught that he that looketh upon a woman to lust after her hath already committed adultery with her in his heart. Thus, for me, the law of chastity would also include not looking at pornography.