야오이 is a genre of 아니메 focusing on highly idealized male x male relationships. It's usually written 의해 women for women, as opposed to bara created 의해 and for gay men. (The men in bara are much more... manly. ^^) Yuri features girl x girl relationships and can be targeted at either men 또는 women.
Be careful with the terms- 야오이 technically boyxboy sex and yuri is girlxgirl sex. The right terms for romance would be shounen-ai and shoujo-ai respectively. Often, however, 야오이 and yuri are used as catch-all terms... which has been known to cause me some confusion. XD
(The picture is NaruSasu... a VERY 인기 야오이 couple. :3)
Simple, English definition: 야오이 is 사랑 between two guys; "gay guys," if 당신 wish. Yuri is 사랑 between two girls; "lesbians," if that's easier to remember.
