Cryptic crosswords are a special kind of crossword puzzles which are especially popular in the United Kingdom. Basically you have to "read them the right way" to find the solution. Usually what they seem to say when read normally is only a distraction. A well-designed cryptic crossword has a logic path to finding the solution through the cryptic clues (the basic principle of fairness).
Cryptic Crossword Rules
A typical cryptic crossword clue consists of two parts: the definition and wordplay. The definition part works similarly like any "ordinary" crossword. It is, in wide terms, a synonym for the answer. Usually the definition appears at the start or end of the clue. Part of solving a cryptic crossword clue is to find out where the boundary between definition and wordplay is.
The wordplay part provides an alternate way to discover the solution. It also helps assure that you pick the right answer to the definition part, making cryptic crossword clues "self-checking". The wordplay could be an anagram or text that should be interpreted in an unconventional way. There are many "code words" and "indicators" the have special meaning in cryptic crosswords. Learning them is crucial to become skilled at solving cryptical crosswords. For example "strange" or "muddled" both are anagram indicators, while a word such as "beheaded" means you should delete a letter.