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[...Suffixes with a -k- generally began as diminutives. In other words, Jan is the Polish form of "John," and Janek or Janko is much like "Johnny." English, however, typically has only a couple of diminutive suffixes, -y or -ie. Polish (and the other Slavic languages) have tons of them. Most have a -k- in there somewhere, or the-k- has been modified by the addition of further suffixes (e. g., -czak, -czyk). As a rule, in surnames a suffix with -k- means something like "little" or "son of."...]

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from the following site:
http://www.polishroots.org/surnames/surnames_endings.htm

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Andrzejczak thus means "little Andrew".