Random error is statistical fluctuation around the true value.
Systematic error is a bias, such as miscalibration or consistent error in observation, such as reading a needle type meter from a non perpendicular angle.
One example of a systematic error is when reading the peak value of a ballistic galvanometer, that you record the maximum value that the needle crosses, a one-directional error, rather than attempting to interpolate the reading, a two-directional error, but one that gives a better result when many observations are made.