They were first given in 1966 (for the year 1965).
The Nebula Awards are given annually by the Science Fiction and Fantasy Writers of America (SFWA) for the best science fiction or fantasy fiction published during the previous year. To be eligible for consideration works must be published in English in the United States. Works published in English elsewhere in the world are also eligible provided they are released on either a website or in an electronic edition. The awards are not limited to American citizens or members of SFWA. Works translated into English are also eligible. (Wikipedia, accessed 28 March 2019)
Active, Associate, Lifetime Active and Lifetime Associate Members are eligible to nominate and vote for the Nebula, Norton, and Bradbury Awards.
Eligibility for published works runs from January 1 – December 31 of a given year. The awards are announced the following spring. In other words, the 2018 Nebula Awards (for works published from January 1st, 2018 to December 31st, 2018) will be given at the Nebula Conference Banquet in May 2019. (How to vote)
Members can nominate and vote. I take it from this that there is no published motivation. The members (most of them active writers themselves) simply like it.
the organization began with a charter membership of 78 writers; it now has over 1,500 members, among them many of the leading writers of science fiction and fantasy. (About the Nebulas)
From this I’m guessing that in the first decade membership was not that high.
Categories for books and articles:
Jack Vance received the Nebula Award for “The Last Castle” (1966), in only the second year the Nebula Awards were given.
The SFWA also made Jack Vance its 15th Grand Master, in 1997.