They gathered fans from all countries, founding there the opportunity to meet old pen-friends (no Internet at that time), buy rare memorabilias, listen to rare music and watch video on large screens. Sometimes, as in New York, an impersonator contest was organized.
Here are some documents.

bob dylan convention dylan revisited 1979 "Dylan Revisited 79", Manchester, UK

bob dylan convention dylan revisited 1980 "Dylan Revisited", 1980, Manchester, UK (quiz list).

bob dylan convention michelstetten, austria "Bob Dylan Festival 1987", 5 & 6 June 1987, Taverne Bauernhof, Michelstetten, Austria.

bob dylan convention the circus is in town   "The Circus Is In Town", flyer (front and back) for the Dylan Convention “Mixed up confusion ‘87” organized on 7th and 8th November 1987 in Chicago, Ill. by The Creatures Void Of Form.

bob dylan convention million dollar bash 1988 "Million Dollar Bash" booklet, Manchester, UK, 5 & 6 November 1988

same, flyer

same, pamphlet with the order form.

bob dylan convention  days of 49 "Days Of 49", Sachas Hotel, Manchester, 25-27 May 1990

same, 4 pages leaflet giving practical informations for the reunion.

bob dylan convention hard times in new york town flyer       "Hard Times In New York Town", 50th Birthday Celebration, New York 24-26 May 1991, New York Skyline Hotel: card cover containing 8 pages outlining the guests speakers and events taking place to mark Bob's 50th birthday celebration

bob dylan convention down along the cove 1993 2-4 April 1993, "Down Along The Cove", in Seattle, Wa., USA

1994, Flyer for "Bringing It All Back Home" in Manchester 20-21 May.

bob dylan convention sweden 1996 1996, "Swedish Dylan Convention", organised by Lars Holm.