Physical meaning of Heisenberg's picture When we present Lorentz's transformations in special relativity we could only say: look! this mathematical transformation does't change physics and so do it whenever you want. But also we can ask "the physical meaning" of this transformation and the answer is actually we change the observer.
In quantum mechanics authors only say: look! this transformation does't change physics and so do it whenever you want. But what is the physical meaning of this transformation?
 A: Lorentz transformation is a transformation to a different reference frame, reflecting the postulate of the relativity theory, that all physical processes run in the same way in all inertial reference frames. 
Transformations between the Schrödinger, Heisenberg and the Interaction pictures in quantum mechanics are not demonstrating any physical relations: they are tools of mathematical convenience, which do not affect the observables (i.e. the quantum mechanical averages). Same could be said about the transformation between the wave mechanics and the matrix representation, or between the first and the second quantization. 
The main physical meaning of these transformation is that the physical reality does not change, just because we use different mathematical tools to describe it.
A: If you must see it intuitively, we can definitely try.
In Schrödinger's picture, the lab frame is fixed, so operators are fixed. Things are like probability fluids flowing around. That's why we measure different results.
In Heisenberg's picture, the object of interest is fixed while the lab frame is rotating. So we are using different operators (at different angles) to measure the same thing and get different results.
Rotating is definitely not a good analogy for all the different ways things could change. So take this intuitive image with a grain of salt.
A: it is simple in schodringer picture the basis states are stationary but the state is time dependent. in heisenberg picture, basis is time dependent but state is stationary.
Let's make an analogy, assume you have a vector in a coordinate system, and you want to rotate it you can do it two ways:


*

*you keep the coordinate system fixed but you explicitly rotate the vector. This is equivalent to Schodriner picture, if you treat the rotation as time evaluation and the vector as the state and the basis as coordinate system.

*you keep the vector fixed but you rotate the coordinate system, and this is equivalent to heisenberg picture. your state does not evolve in time, but you basis which is the coordinate system in this analogy rotates.
both of them are equivalent because, in both of them, the change of angle between the vector and the axis' is same.
so heisenberg and schodringer picture, is nothing but passive versus active transformation.
