please explain what the year of the dragon means

The year of dragon means different for people born in the year of different animal signs. You may see details at https://www.travelchinaguide.com/intro/social_customs/zodiac/

It means Unpredictability, parties, fun, music, arguments, strong minded personalities are highlighted, power, and uproars even. Water cools the dragon giving it a cool feel, but can still be a rough year.

it has water wood and earth so depending on whats bad/good for you
it can be mixed. 1/2 months good 1/2 bad

unlike a pure animal such as rat (water only) or rabbit (wood only)

What does it mean to be born in the year of the dragon. I was born in 1964 and my wife in 1984, are we born in the dragon year or not?

It has no special meaning of born in the year of Dragon. Just like the constellation in Western Culture, Chinese culture has twelve animals represent twelve years. Different people born in different years have certain characeteristics.
For you, you were born in the year of dragon if you born before Feb 2, 1964, otherwise, you were born in the year of rabbit.
For your wife, she was born in the year of pig or rooster year.