What does "Rabbit" mean on 1st of June

My english teacher told me, that is common in England to say "Rabbits" on the 1st of june.

What does it mean?

where does this tradition come from?

Does the people say it only on the 1st of June?

I hope that I'm at the right place to make that question.

Rabbit, Rabbit, Rabbit is a superstitious wishing game:

a common British superstition which states that a person should say or repeat the word "rabbit" or "rabbits", or "white rabbits", or some combination of these elements, out loud upon waking (or first moment) on the first day of the month, because doing so will ensure good luck for the duration of that month.

_{Wikipedia.org}

"It is roughly the superstitious equivalent of the nursery rhyme Star Light, Star Bright:

Star light, star bright,
The first star I see tonight;
I wish I may, I wish I might,
Have the wish I wish tonight.

The superstition of hoping for wishes granted when seeing a shooting or falling star may date back to the ancient world. Wishing on the first star seen may also predate this rhyme, which first began to be recorded in late nineteenth-century America. The song and tradition seem to have reached Britain by the early twentieth century and have since spread worldwide.

_{Wikipedia.org}

It seems English-speaking parents use wishing games like Rabbits, Rabbits, Rabbits and Star Light, Star Bright to nurture a sense of persistent optimism in their small children. "As with most folklore, which is traditionally spread by word of mouth, there are numerous variants of the superstition, in some cases specific to a certain time period or region:"

• When I was a very little boy I was advised to always murmur 'White rabbits' on the first of every month if I wanted to be lucky. From sheer force of unreasoning habit I do it still—when I think of it. I know it to be preposterously ludicrous, but that does not deter me." – Sir Herbert Russell, 1925.[13]
• "Even Mr. Roosevelt, the President of the United States, has confessed to a friend that he says 'Rabbits' on the first of every month—and, what is more, he would not think of omitting the utterance on any account." – Newspaper article, 1935.[14]
• "On the first day of the month say 'Rabbit! rabbit! rabbit!' and the first thing you know you will get a present from someone you like very much." Collected by the researcher Frank C. Brown in North Carolina in the years between 1913 and 1943.[15]
• "If you say 'Rabbit, rabbit, rabbit' the first thing when you wake up in the morning on the first of each month you will have good luck all month." Collected by Wayland D. Hand in Pennsylvania before 1964.[15] "Say 'Rabbit, rabbit, rabbit' at the first of the month for good luck and money." Collected by Ernest W. Baughman in New Mexico before 1964.[15]
• "...it must be 'White Rabbit' ... but you must also say 'Brown Rabbit' at night and walk downstairs backwards." Reported in a small survey that took place in Exeter, Devon in 1972.[16]
• "Ever since I was 4 years old, I have said 'White Rabbits' at the very moment of waking on every single first day of every single month that has passed." Simon Winchester, 2006.[17]
• "...the more common version 'rabbit, rabbit, white rabbit' should be said upon waking on the first day of each new month to bring good luck." Sunday Mirror, 2007.[18]

_{Wikipedia.org}

Although there is no firmly established correlation, it is possible that this superstition is rooted in the ubiquitous icon of three hares:

a circular motif appearing in sacred sites from the Middle and Far East to the churches of Devon, England (as the "Tinners' Rabbits"), and historical synagogues in Europe.

_{Wikipedia.org}