A few words about ethymology:
The word являться is a reflexive (ends in a -ся) counterpart of the outdated verb "являть" that itself has been lost to the ages.
The verb basically meant "to bring" like:

И пришёл Христос и явил чудо - больные исцелялись, а мертвые оживали.
(Christ came and made/brought a miracle -- the ill would recover and the dead would come alive)

According to the concept of reflexive vebs (which actually are called "возвратные" глаголы in Russian, which better reflects the idea behind them -- "возврат" means "return"), so the action that the verb denotes "returns" to the subject, like "являться" is "являть"-bring but returned to the subject who "являет", so it's like "bring himself", which perfectly fits in the concept of reflexive verbs in Russian.

A few more reflexive:
Катать (take someone for a drive) -- кататься (take yourself for a drive)=ride
Качать (sway, swing, rock something) -- качаться (swing yourself on something)=a baby "качается" on a child's swing, I can try to "качаться" on a door if I grab it by the top and hang on it (unfortunately it's going to fall apart if I do that but as a child I used to "качаться" hanging on something).
Вернуть (return, hand something back) -- вернуться ("return yourself to somewhere")=come back


So являться (to be) = "Our enterprise has brought itself as one of the most profitable companies in Europe"
And являться (show up) = "He brought himself home drunk late in the evening" = Явился домой пьяный поздно вечером.