BED files provide the coordinates of regions in a genome; most basically chr, start and end, however other fields provide greater detail.
bedGraph files give coordinate information, as in BED files, but a fourth column can be a number. The files are often used to show coverage depth of sequencing over a genome. For example, bedGraph files can be converted to bigWig (a binary indexed version) that can be displayed on the UCSC Genome Browser. Pgibas' links are where to go for more information.
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