A bigender person is someone who identifies as two genders. A common misconception is that bigender people always only identify as "male" and "female" but they can identify as two non-binary genders or a binary and non-binary gender. Bigender people may experience switching or simultaneous identification, but what makes it distinct from gender fluid is that gender fluid persons have "fluid" gender identity that cannot be pinned down and may consist of multiple genders mixed together. Bigender people however have two distinct genders.
Some bigender people have the desire for sex traits of their two identifying genders. Some identify as angenital or sexless. Some switch between gender presentations. Some are androgynous. Gender dysphoria, both social and physical, can be very distinct for bigender people. For some, HRT and/or surgery are not adequate to help alleviate dysphoria, and many different methods are sought by all bigender people to make them feel comfortable and happy.
Some are happy without any need for bodily changes and identify as whatever genders they think fit them best. Physical dysphoria is not a prerequisite for being bigender. Identifying as two distinct genders is. Dysphoria, however, is something many bigender people deal with and should not be taken lightly or mocked. Use preferred pronouns and name(s), and support your bigender friends.