This is one of the best known geometric illusions. It consists of two lines which are equal and bordered by fins. The one with the outgoing brackets is seen as larger than the one with the inward brackets. It was first reported in 1889 by Franz Muller-Lyer and has been studied repeatedly over the years. For instance, some theorized that the feedback from eye scans contributed to the effect, the inward fins truncating a scan and the outward fins permitting a wider scan. Since tachistoscopically presented lines (faster than any possible scan) still elicit the illusion, this hypothesis is not tenable.
More acceptable explanations center on the notion that the brackets are depth cues which are centrally processed leading to the judgement that one line is closer than the other. Since they both create retinal images of equal length, the line viewed as closest is seen as smaller.