The verb являться in the imperfective aspect essentially means "to be" and is primarily used to define a subject in more formal or official speech and in periodical texts. Of the two or more nouns linked by the verb являться, the subject defined is in the nominative case and the definition ascribed to it is the instrumental case.
An expansion of our product line is our principal task.
The contract is the basic form of legal agreements.
Mr. Brown is the president of a large company.
Note that являться is almost exclusively used in the third person, as first person usage would reflect a certain pomposity.
means "to appear," "to report," or "to arrive" somewhere in an official capacity, where movement from one place to another is involved.
It answers the question Куда? (Where to?). Появиться means "to appear" or "to show up" in a place, and answers the question Где? (Where?).
Where do I have to report for a pass?