Here is an annotated image from the Wikipedia article on circular polarisation.
All that I have done is added three spatial coordinate axes: x, y and z.
This is a very much simplified diagram of what is actually happening and shows "a wave" travelling in the z-direction with the spatial values of x and y constant.
The other parameter which is constant is the time.
This is a snapshot of the wave at one instant of time.
However it is not a snapshot which could ever be taken with a camera in that it shows how the electric field (vector) varies with z keeping x and y constant.
Since the wave is travelling in the z direction the electric field can only have components in the x and y direction but these components vary as the value of z changes.
So at one particular point in space (x,y,z) the electric field must be in the xy plane (orthogonal to the z direction) and the electric field can only vary with time in this plane.
That is the electric field can only have components in the x and y directions but not in the z direction.
I did say that the diagram is simplified because I could have drawn another parallel wave with a different value of x incident on the Polaroid as shown below
but still the variation of the electric field with time can only be in the xy plane.
Instead of two just imagine more and more such waves until you have a continuum equivalent to a parallel beam of light travelling in the z-direction but with the electric field only varying in xy planes.
The addition of two simple harmonic motions at right angles to one another produces what is called a Lissajous figure.
Use this simulation to show the result of such an addition by making the x and y frequencies and amplitudes the same and having a zero phase difference to get a straight line (linear polarisation).
Then change the phase difference to $90^\circ$ produced by the wave plate and obtain a circle (circular polarisation).