What is the physical meaning behind the concept of shear lag in fibre reinforced composite structures or the concept in general for any structure?
Here is how I visualize what is physically happening (for steel sections):
As you get closer to the connection to the gusset, all the force needs to be transferred through the bolts, so the stress has to flow toward the connected portion of the angle. In the limit, (L = 0) the net effective area would simply be the net area of the connected portion of the element.
I can't speak to fiber-reinforced composites, but the general concept of shear lag is summed up in the AISC 360-10 Specification, Commentary Section D3 as such:
Shear lag is a concept used to account for uneven stress distribution in connected members where some but not all of their elements (flange, web, leg, etc.) are connected. The reduction coefficient, $U$, is applied to the net area, $A_n$, of bolted members and to the gross area, $A_g$, of welded members. As the length of the connection, $l$, is increased, the shear lag effect diminishes. This concept is expressed empirically by the equation for $U$. Using this expression to compute the effective area, the estimated strength of some 1,000 bolted and riveted connection test specimens, with few exceptions, correlated with observed test results within a scatterband of ±10% (Munse and Chesson, 1963). Newer research provides further justification for the current provisions (Easterling and Gonzales, 1993).
Basically, shear lag is a concept where the forces in a connection require a certain length to properly "get out." This is partially dependent on the relative stiffness of the connection vs. the direction of the application of the load.
For example, consider the figure below from the AISC 360-10.
The example on the left is more impacted by the effects of shear lag since the force in the connection has to transfer along the length $l$ of the weld. The $U$ value would likely be less than 1.0, indicating the influence of shear lag.
In the middle example, the weld at the end of the angle is perpendicular to the force. In this case, the $U$ value would likely be 1.0 (assuming the outstanding leg of the angle is also welded similarly) since the force is transferred uniformly to the perpendicular weld.
Table D3.1 of the AISC 360-10 tabulates the calculation of different $U$ values based on the connection geometry. I have pasted a snippet of it below for a couple examples. Your code of record may vary depending on your country and jurisdiction.