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When oxidising primary alcohols, $\ce{K2Cr2O7}$ is used because it's a useful & readily available oxidising agent.
Why does the sulfuric acid need to be added? Does it have to do with the acidity of the resulting dichromate solution? How would this facilitate the oxidation?
It protonates the chromic acid to form an oxonium ion, increasing positive charge at the chromium center.
Using $\ce{H^+}$ typically protonates the electrophile, making it more electrophilic (more electron deficient = more electrophilic), just like with acid-catalyzed esterification. In fact, you're making a chromate ester in this reaction.
See the first step here in this image (and the rest is related, also):
Image source
