Start from the verb mow: cutting grass down flat and even, sweeping across a field or a lawn so that everything is left at the same short height. Add -er and you get 'the one that does the mowing'. English lets that -er point at a machine as easily as at a person, so the picture is a thing moving forward over grass with a blade turning underneath, leaving a clean strip behind it — whether that thing is a red machine you push, or a man with a long blade walking through the field.