Nowadays, many models of DSLR come with APS-C sized sensors which are smaller than the full-frame 35mm. For this reason, a cropping effect exist.
All diagrams used below are edited from here.

Size of the APS-C sensor varies depending on brands and models, therefore the crop factor also varies. Crop factor is represented by a multiplier value (e.g. 1.3x, 1.5x, 1.6x). Look at the diagram above again. If you think from another point of view, assuming a fixed focal length, the image projected on the APS-C sensor has a zoom-in effect compared to the image on the full-frame sensor. In other words, the image on the APS-C sensor seems to be taken from a lens with a longer focal length.
How much longer in focal length? Multiply the actual focal length by the crop factor then... It's better to explain with diagram. =Þ

50mm focal length on the APS-C sensor.
50 × 1.6 = 80

80mm focal length on the full-frame sensor.
Comparing both resulting image.
This can be good news for APS-C sensor users as more zooming effect is added on to their lens, but not so good for those who want to take wide angle shots. There's also benefit to lenses that are designed for APS-C sensors as manufacturers take advantage of these smaller sized sensors to produce lenses that are more compact. Though not compatible for use with the full-frame camera, but cheaper to produce and more affordable by consumers.

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