Someone who believes themselves to be heterosexual, but has thoughts about sex with another person of the same gender.
When a person who identifies themselves as to having a preference for engaging in sexual relations, and/or having affections for one particular gender, but has thoughts or desires to seek a similar type relationship with the other gender.
If a man, who identifies himself as preferring to be romantically involved, sexually involved with females, but also has an urge to see what it is like with another male, he could be classed as being bi-curious.
This 'attraction' is more about curiosity than any deep emotional or hidden sexual preference. It is like trying out a different type of food such as Chinese when one is used to Mexican only.
Noteworthy: Bi-curious is more about a person's natural refusal to be held captive by a society definition of one's sexuality.
In some circles of thought, it is considered that a person being curious shows a disposition to being pansexual or bisexual already, and that it is merely a stepping stone to finally defining their own sexual orientation.