Two objects are congruent if they have the same dimensions and shape. Very loosely, you can think of it as meaning 'equal', but it has a very precise meaning that you should understand completely, especially for complex shapes such as polygons.
Two line segments
are congruent if they have the same length. But they need not lie at the same angle or position on the plane.
Two angles
are congruent if they have the same measure. So if two separate angles have measures of 30° and 23°
for example, they are not congruent
because they have different measures. Congruent angles may lie in different orientations or positions.
See Congruent Angles
Two circles are congruent if they have the same size. The size can be measured as the
radius,
diameter or
circumference.
They can overlap.
Congruent polygons
have an equal number of sides, and all the corresponding sides and angles are congruent.
However, they can be in a different location, rotated or flipped over. So for example the two triangles shown above
are congruent even
though one is a mirror image of the other.
See Congruent Polygons
Congruent polygons should not be confused with similar polygons which can be in the same proportions but different sizes.
The symbol for congruence is 
If A and B are two objects being compared, such as line segments, angles, triangles etc, then the statement
is read as "A is congruent to B".
If there is a diagonal line through the symbol, this means 'not':
is read as "A is not congruent to B".