Open and closed circles are used to mark the end points of intervals.


If the circle is open, it means the end point is NOT included in the interval,
but if the circle is closed, it means the end point is included.


Consider the interval .  In this interval, the low endpoint, the 3,
is not included because you have a 'less than' sign.  The high endpoint, the 6,
is included because you have a 'less than or equal' sign.  It is the presence
or absence of the 'or equal' part that determines whether the circle is closed
or open.


The interval  would be marked on the number line with an open
circle at 3, a closed circle at 6, and a heavy line connecting the two.