Please read the help file. Then search for existing discussions (http://community.qlik.com/search.jspa?q=lookup+applymap) and read those. For example the discussion What are the advantages of Applymap() over lookup(). If after that you still have questions ask about the details you don't understand yet of couldn't find an answer to.
Applymap() is used to lookup only one column, In mapping table there should be a maximum of two columns (one for Key and other is value), but in lookup() you can have any number of columns (with one key and any number of value columns). This is the main difference.
Check this thread
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