Consider these definitions:
The figure below shows an example of a dynamic mechanism:
In this case the truss is free to move as shown even if the bars that make up the truss do not change length. To solve this problem you need to do some dynamic analysis.
Adding a diagonal to the truss above removes the mechanism, because the diagonals change length during the motion. Thus, if the diagonal bar only changes shape a fixed amount, the motion is restricted and the truss is static:
One easy way to see difference between these two trusses, is that the mechanism has a square structure while the static truss is made up of two triangles. It is a general rule that three sided regions do not contain mechanisms, while four or more sided regions may. However, it is still possible to have a mechanism in a truss made up of all triangles. Consider the truss below:
This truss has a mechanism because the two triangles are only connected at one point. This truss can be made static by either adding a bar between the two middle lower joints or adding a horizontal restraint at the lower right node.
Mechanisms in a complicated truss can be difficult to spot at times. If there is mechanism in your truss you will either get an error during the solution or the solution will have very large displacements (small displacement magnification) that do not make physical sense. These are essentially the same errors as those caused by Boundary Conditions that do not restrict all the rigid motions of the truss. See What happens if I have not restricted all rigid body motions? for more details on these types of errors.