It is part of the official style of speech. Try to avoid it in informal speech at all costs because it makes you sentences longer and less expressive. Sometimes you can replace it with a more concrete verb, sometimes with "to be" (есть, был, будет). But most of the time you will you dash mark (тире). Some examples: 1. Он является королём. This sentence is grammatically correct but too heavyweight to be used in real speech. 2. Он — король. (He is king). Long word is replaced with a long pause. Easier to write, easier to pronounce. 3. Он является представителем профсоюза => Он представляет профсоюз. But you can freely use this word in other meanings e.g. "to arrive".

The word "is" does exist, we just drop it in present tense. And you won't often hear it in colloquial speech, but it can be used in more complex writing style, often in documents and textbooks, for example. Sentences with "является" sound more serious and formal. Note that after "является" genetive case is used. It feels kinda like this: Это является серьёзным нарушением. - This constitutes a severe violation. Это серьёзное нарушение. - This is is a severe violation. But "Она является красивой" just sounds wrong, because it's not something that you can make "serious and official".

Sometimes it is used as "is", especially in formal writing or when you make a conclusion. For example, Является ли законным использование ... ?( Is it legal to use... ?) Список стран, где английский является официальным языком..... ( The list of countries where English is an official language...) Еще одним следствием этих результатов является то, что... - One further consequence of these results is that... But it seems to me that it also could be used in informal speech too when you want to highlight something: Из всех искусств важнейшим является кино However it is not very common.

In an informal conversation "Каждое слово в русском языке является новым для меня" is better expressed as "Каждое слово в русском (языке) для меня новое" ))

It is probably the least formal version of the Russian word for 'is'. The other two, off the top of my head, are 'есть' and 'суть'.