Fixed pattern noise simply refers to a constant non-uniformity across a digital sensor, that causes a pattern to appear in images that is generated by the device itself. The pattern is not caused by an incoming signal. While it would be better if it were not present in the first instance, there are methods available to removed or at least minimise this unwanted pattern.

Manufacturers often employ on chip methods such as double correlated sampling, which measure a pixel's voltage before and after image integration to cancel and residual capacitance caused by thermal noise. 

Design of the sensor also affects the device's uniformity. In CCD sensors each pixel value read by just one analogue to digital converter, hence there is excellent uniformity in the readout process. In CMOS sensors each pixel is doing its own conversion, so uniformity is lower.

Off chip methods essentially come down to flat-field calibration. Applying a flat field correction not only removes any optical vignetting and shadowing from dust motes and the like, it also maps pixel sensitivity variations.  Flats fields are simply good practice as they also restore the relative illumination differences within an object or scene.

Fixed pattern noise unfortunately, is not always "fixed", and can vary slightly in amplitude or spatially to make it extremely difficult to remove from very low signal images. Dithering or shifting the data collected to different pixels locations across multiple exposures can pay dividends, particularly with high spatial frequency pattern noise.(i.e. when the pattern repeats over just a few pixels)

You can test your camera for fixed pattern noise by simply median combining several dark frames, say of 30 seconds duration, then convert the image using a fast fourier transform (FFT) filter. Any repeating pattern will be quickly revealed by the FFT filter as seen in the images below.