"Symmetry"
is a recognition of the matching-ness of the parts of a shape.

For instance, the
human body is said to have "bilateral" (two-sided) symmetry,
because the left and right halves of the body mirror each other,
as you can see in the image to the left.

But this symmetry
applies only to the basic framing structure of our bodies; much
of our insides, our organs, don't match, as you can see in the
image to the right: watch the liver (brown) and the stomach (pink)
change sides when the organs are flipped.:

The
dotted line running down the middle of the left-hand graphic above is
called "the axis of symmetry".

If
you think of the bilateral-symmetry picture as being drawn on
a sheet of transparent plastic with a shish-kebob skewer punched
through the dotted line, you could twirl the skewer (and thus
the sheet) 180° around and end up looking at the same picture,
but from the other side of the plastic sheet:

(Note:
If this animation experiences occasional breaks, you're probably
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browser.)

A
figure has as many symmetries as its plastic sheet can have skewers.

For
instance, a rectangle can be twirled through its middles, so a
rectangle has two symmetries.

A
square can also be twirled along its diagonals, so a square has
four symmetries.

A
triangle might have one or three lines of symmetry, but usually has none:

one
line of
symmetry

three
lines of symmetry

no
lines of
symmetry

...and
a circle has infinitely-many lines of symmetry, since any line through
its center (any diameter) is also an axis of symmetry.