In-Plane Stiffness
Consider the examples below.
The wall with boundary elements (left) has very high stiffness in the direction along the wall, as indicated by the red arrow. Likewise, the I-beam (middle) clearly has higher stiffness in the indicated direction perpindicular to the flanges. Finally, a concrete floor slab will usually have high in-plane stiffness along the horizontal plane of the slab.
Out-of-Plane Stiffness
The examples shown below also have an axis of weakness, which is shown below:
For the wall, it would be much weaker when loaded in the out-of-plane direction. Similarly, it is easy to imagine that the I-beam and slab also have low-stiffness in the indicated directions.
Example
Consider the following example of a wall (plan view).
Iyy = bd^3/12 = 30(500^3)/12 = 312,500,000 cm^4
Ixx = 500(30^3)/12 = 1,125,000 cm^4
Iyy / Ixx = 177.7
Therefore the stiffness about the Y axis (in-plane) is significantly higher than the stiffness about the X-direction (out-of-plane).
Final Comments
In analyses and design, we should be mindful of the different strengths and weaknesses of certain sections, but we can also use them to our advantage. Furthermore, certain sections may not have a clear strong or weak axis. For example, Square Hollow Sections (SHS) have the same stiffness in both directions.