Consider an electron sitting at the origin of a coordinate system. Let an unpolarized light travelling in the $z$-direction excite the electron at the origin. The motion of the electron can be thought of as two independent oscillatory motions, one along $x$-axis and the other along $y$-axis.
If we look at the scattered radiation along $y$-axis, there will be none due to the motion along the $y$-axis. The scattered radiation that reaches the eye when viewed along $y$-axis is due to the motion along $x$-axis. It is true that an electron oscillating in the $x$-axis will give rise to maximum intensity when viewed along $y$-axis.
I cannot understand why an electron oscillating along $x$-axis will produce electric field polarized along $x$-axis.