What it means:

in a jam; in a difficult or unpleasant situation

How Shakespeare used it:

In The Tempest, King Alonso asks his jester, Trinculo, "How camest thou in this pickle?" And the drunk Trinculo – who has indeed gotten into trouble – responds "I have been in such a pickle since I saw you last ..." (Act 5, Scene 1)

One theory has it that the phrase in a pickle entered English from an old Dutch expression that translates as something like "sit in the pickle," i.e., get stuck in the brining solution used to make pickles.

Shakespeare is probably also playing on the fact that alcohol, which is sometimes used in the pickling process, has certainly contributed to the pickle Trinculo is in.

Modern example:

"Has the NYT got itself into a pickle over digital editions on Kindle and iPad?" — adamhodgkin on Twitter, May 6, 2010