What does linear dependence (among vectors) actually mean geometrically? Does it have any geometrical meaning? Also, I would ask is there any physical entity described by a linear combination and or linear dependent vectors?
 A: Geometrically, the span of a set $\{w_1\dots w_k\}$ is a subspace of the whole vector space. Picture a line through the origin, or a plane through the origin of 3-space.
If adding $v$ to a set $\{w_1\dots w_k\}$ results in a linearly dependent set, then that means that $v$ lies in the subspace generated by the $w_i$. In this sense, dependence indicates membership. Consider: adding 0 to any set makes the set linearly dependent, hence 0 is contained in all subspaces. If a set generates the whole space, then of course any vector added will be dependent, because it is guaranteed to belong to the span.
Every vector in a vector space is expressible with arbitrarily ridiculous combinations of dependent vectors. Say: $v=w-w+x-x+0+0+v$.
More interestingly, any vector is expressible as a unique linear combination of basis elements of a vector space. This uniqueness is both attractive and practical.
I guess this depends on what you intended to mean by "physical entity," but try this. Usually we think of unit vectors along orthogonal coordinate axes as "measuring sticks," and measurements of distance that we make in 3-space are linear combinations of these three rulers (which retain their sense of direction).
