The concept of a parabolic trough can be best understood if you take a look at the picture below which gives an overview of a section of the parabolic trough. Upon seeing the picture you will intuitively realize the reason for the name given to this arrangement. The term parabolic signifies the shape and it is a trough since it is used for collection of sunlight.

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When sunlight falls on the parabolic shape which is coated which is having a reflective material so that it absorbs the minimum possible light but reflects the maximum possible light that falls on its surface; the sunlight gets reflected and due to the shape of the trough it concentrates at a point which is the focus of the concave shaped trough. There are absorbing tubes running across the length of these troughs passing through the foci of the series of troughs.
These pipes have water running in them and you can very well imagine who the system works. Since the sunlight is reflected at the focus and the tube is located at the same point, it absorbs most of this light since it is made out of special materials which absorb the heat. This heat naturally gets transferred to the water flowing inside these tubes and gets transported to along with the flowing water
This water is then utilized as boiler feed water which generates steam and that steam is used to turn the turbines which in turn provide rotary power to the electric generators. Of course the water itself is not sufficient to generate steam and the boiler also consumes fuel to convert the water into steam, yet the pre-heating of water using the freely available sunlight saves a considerable amount of fuel.
Hence we see that parabolic trough solar power collectors help to increase the efficiency of conventional power plants by helping to heat the feed water by a significant amount. Another advantage of this arrangement is that when the sunlight is not fully available due to weather conditions, the plant does not get effected since it can still generate steam by using more quantity of fuel during that time period.