The term Seventh Millenium refers roughly to the present millenium, starting variously in 1962, 1979, 2001, or some other milestone date. It refers to the beginning of human urbanization and writing and recorded history which is variously dated as having begun over 6000 but under 6500 years ago.
It is a deliberate attempt to avoid cultural bias in long term dates.
Interestingly, the term is generally acceptable to Christians who accept a very short history of the world (whose creation would be in 4004 BC by some estimates). Some suspect the term for this reason. Others consider it a happy coincidence of written records and the Biblical record that reduces the least rational argument and presumably attracts those who believe in creationism. For them it would emphasize common roots in Adam, Eve and Noah rather than the overt cultural and religious distinctions that arose later. The term may have been coined specifically to focus on human common origins.
All existing calendars are biased towards some culture or religion. For instance, the date "2003 CE" for "2003rd year of the Current Era" is a loosely disguised "Christian Era" which is in fact dated from a somewhat questionable dating of the birth of Jesus long after the fact. It could just as easily be said to date the calendar back to the creation of the month of August to honour Caesar Augustus, consolidator of the Roman Empire. Christian and Roman society in fact merged institutionally over several hundred years, with Christian traits taking ascendance as of the Sack of Rome in 1410. It was shortly after that that the dating from the birth of Christ became standard, and superceded that from founding of Rome.
The use of the term Seventh Millenium is most common among secular futurists, and those who consider themselves to be world citizens. These often have an agenda of technological globalization but oppose a more corporate or religious millenial vision (which exist regardless of whether the present millenium is the third, or seventh, or even the first).