This word is grammatically incorrect. It is used by conservatives that believe it is ok to discriminate against transgender people. The "Transgendered" are women that were born with male sex characteristics/men born with female sex characteristics (or non-binary people whose gender doesn't fit the binary). This isn't a made up story, as doctors can prove it with
MRI scans.
Transgender is similar to
intersex, but while for intersex people the problem is phisycal (reproductive organs partially/not functional) for the transgender person the problem is neurological.
Despite their physical attributes, trans women are women and
trans men are men.