A countertenor is a male classical singer whose range matches a contralto or mezzo-soprano, usually about E3 to E5. Most countertenors sing at least the upper half of that range in falsetto or a reinforced head voice and use chest voice for the lowest notes. The name comes from the contratenor altus, the line written above the tenor in Renaissance music, which also gave us the word 'alto'.
The voice faded from opera when castrati took the high male roles, but it survived in English church choirs. Its modern revival began with Alfred Deller in the mid-20th century; Benjamin Britten wrote Oberon in A Midsummer Night's Dream (1960) for him, and Russell Oberlin led the way in the United States. Since then singers such as James Bowman, Andreas Scholl, David Daniels, Philippe Jaroussky, Iestyn Davies, Anthony Roth Costanzo and Jakub Józef Orliński have made countertenors a regular sight in opera houses.
Pop has plenty of high male singing, from the Bee Gees' falsetto hits to soul and R&B ad-libs, but those singers are not countertenors in the classical sense. The term describes a classical voice type and the repertoire that comes with it, not simply a man who sings high.