Являться is used in formal texts, like laws or technical documentation, or scientific research. It is used for clearness, for every sentence and every clause to have at least one verb. In a similar way, the verb иметь is used in formal contexts instead of the informal construction у Х (Gen.) [есть] Y. In works of fiction, являться and иметь are used rarely, mostly for creating a formal atmosphere.
For example, in a pop song Вселенная ("Universe") by the band Иванушки Int. (lyrics), they enumerate different things and after each of them they add тоже является частью Вселенной, "also constitutes a part of the Universe". Here, является brings in a kind of scientific tone which contrasts with the simple things they mention, like "a barman, a girl, a taxi, etc. also constitute a part of the Universe".
UPD: Also, in the case of X [есть/—] Y which means "X=Y", both X and Y are in the Nominative case, and Russian has free word order, so sometimes it is hard to tell what in the sentence is X and what is Y, and it can be important, since in scientific discourse X=Y doesn't necessarily mean the same as Y=X, e.g. 'философы — лжецы' ≠ 'лжецы — философы'. In such cases, являться helps to remove the ambiguity, since with it X is in the nominative and Y in the Instrumental case:
Философы являются лжецами.
Лжецами являются философы.
Both sentences mean "Philosophers are liars", and not "Liars are philosophers".