(terms defined without too much sundialling jargon!)

Altitude - angle up from the horizon of the centre of the apparent disk of the sun or moon.
Arctic Circle - imaginary line around the earth at about 66 degrees 33 minutes in the northern hemisphere which defines the boundary of the Arctic.  It marks the start of the area where, for at least one day each year, the sun doesn't set (on or around 21 June) or doesn't rise (on or around 21 December).
Azimuth - angle along the horizon measured from true south.  Angles to the west are positive, to the east negative.  So west is 90 degrees, east -90 degrees and north plus or minus 180 degrees.
Dial Plate - the flat structure where the dial furniture and hour lines lay
Equation of Time - difference between solar time (where the sun actually is in the sky) and Mean Solar Time (where the sun would be in the sky if the earth's rate of rotation were constant and there was no inclination between the equator an the orbit of the Earth) This can vary from +14 minutes to -16 minutes.  The chart/graph showing these correction figures is usually somewhere close to the dial to allow for a calculation of clock time (local mean time).  More detailed explanation with links to pictures of an analemma
Equinox - days when the sun rises and sets at approximately the same times all over the earth (literally means 'equal nights').  The amount of daylight is not the same everywhere, however.  Before sunrise and sunset at the Equator, for example, there is a short time of twilight, as opposed to arctic/antarctic regions where there is a very long twilight due to the gradual angle of the suns rising/setting. 'Vernal' or 'Spring' Equinox is around 20-21 March and 'Autumnal' or 'Fall' Equinox is around 22-23 September (in the northern hemisphere).
Furniture - common features which appear on many dial plates, eg location name, latitude, date of installation, Equation of Time table or graph, motto, maker/designer, sponsor/benefactor
Gnomon - (pronounced no-mon) the part of the sundial which casts the shadow
Hour Line - line on a dial plate indicating the shadow position at a specific time.  It is circular on the LYB sundial and shows half hours, quarter hours and three minute intervals
Polar Night - portion of the year when the sun does not rise above the horizon.  Its length ranges from twenty hours at the Arctic/Antarctic Circles to 179 days (almost six months) at the North/South Pole.  In Longyearbyen, it lasts for 112 days, or just over three and a half months.
Solstices - summer solstice is on or around 21 June (Northern Hemisphere), when the sun reaches its highest altitude for the year.  Usually coincides with the longest day of the year.  At this latitude, that is not relevant, however, as the days have been the same length for almost two months!   Winter solstice is on or around 21 December when the sun reaches its most negative altitude for the year.  These days are reversed in the Southern Hemisphere.
Summer Time - one hour ahead of British Summer Time and two ahead of Greenwich Mean Time.  Starts end of March and ends at the end of October.  Summer Time in Longyearbyen doesn't have much purpose except for the convenience of keeping the same clock time as the rest of Western Europe.  You must add an hour to the reading of the Longyearbyen Sundial to allow for Summer Time.