This was a certificate issued by the Independent Order of Odd Fellows, a fraternal group loosely inspired or based on Freemasonry; it's the American version of the original Order of Odd Fellows in the United Kingdom. By the end of the 19th century, they were the largest fraternal organization in the US, bigger than the various Freemason societies, but declined during the Great Depression. You can read a brief history of the organization here, and the Oddfellows themselves are still around as an organization, so you can read their history in their own words on their website.

The rest you can pretty much read from the paper: in 1944, the wife (whose name I cannot decipher - Frances E. Clivens?) of a member (Harry squiggle Clivens?) was inducted in March 1944 at the Waterbury, CT lodge. These were very common certificates certifying membership for fraternal orders of the period, and as you can see mass-produced to order.