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I would like to know what is the meaning of 13pt in here:

\documentclass[a4paper,13pt]{article}

My first guess was that it was the size of the characters, but changing the number does not seem to do that.

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You most likely receive a message in your output (.log) saying LaTeX Warning: Unused global option(s): [13pt] – Werner Sep 12 '12 at 13:54
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An option is just a string of characters; the class does nothing with unknown options, and 13pt is unknown to article, which has only 10pt, 11pt and 12pt for choosing the main font size. – egreg Sep 12 '12 at 13:54

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13pt in \documentclass[a4paper,13pt]{article} means the font size. But unfortunately article class offers only 10, 11 and 12pt sizes. If you want bigger font you may switch to KOMA class (scrartcl) or extarticle or memoir class. Also you may try the packages --- scrextend, anyfontsize, fix-cm to change the font sizes in other document classes.

For details on these units of font size please see this question and answers.

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None of these classes offers 13pt, AFAIK. – egreg Sep 12 '12 at 13:56
@egreg: true. I didn't mean it. I said only bigger fonts :) – Harish Kumar Sep 12 '12 at 13:57
thanks, and what are the units of the size then? I mean, for example how many millimeters are 10pt? – inquisitor Sep 12 '12 at 14:05
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@inquisitor: TeX uses the traditional printing points system (Ie not Adobe), where 1 inch (or 25.4mm) is 72.27 points. – Brent.Longborough Sep 12 '12 at 15:20
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Wikibooks provide a nice conversion table between different ways of measuring length/size. – mythealias Sep 12 '12 at 16:48

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