
wesentlich
essential
Of fundamental importance, very important or decisive; essential.
Gegenseitiges Vertrauen ist ein wesentlicher Bestandteil einer guten Freundschaft.
Mutual trust is an essential part of a good friendship.
essential / significantly
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essential
Of fundamental importance, very important or decisive; essential.
Gegenseitiges Vertrauen ist ein wesentlicher Bestandteil einer guten Freundschaft.
Mutual trust is an essential part of a good friendship.

significantly
Used as an adverb to express a considerable difference; clearly, considerably, much.
Seit dem Training hat er sich wesentlich verbessert.
Since the training, he has improved significantly.

essentially
A fixed expression meaning 'basically', 'mainly', or 'in the most important points'.
Der Plan bleibt im Wesentlichen unverändert, nur ein paar Details wurden angepasst.
The plan remains essentially unchanged; only a few details were adjusted.
The word 'wesentlich' (essential) derives from 'das Wesen' (the essence/nature), which means 'die Essenz' (the essence) or 'der Kern' (the core) of something. Something that is wesentlich therefore concerns the core and is thus fundamentally important.
Die wesentliche Frage ist, ob wir genug Zeit haben.
The essential question is whether we have enough time.
You can recognize the function of 'wesentlich' (essential/significantly) by its position: as an adjective, it comes before a noun; as an adverb, it comes before another adjective (often in the comparative); and as a fixed expression, it appears as 'im Wesentlichen' (essentially).
Das ist ein wesentlicher Punkt in der Diskussion.
That is an essential point in the discussion.
As an adverb, 'wesentlich' (significantly) means something like 'deutlich' (clearly/significantly) or 'viel' (much) and is used to emphasize a large difference. It very often comes before a comparative.
Die Preise sind dieses Jahr wesentlich höher.
Prices are significantly higher this year.
The fixed expression 'im Wesentlichen' (essentially) can stand at the beginning of a sentence (position 1) or inside the sentence. If it stands at the beginning, the conjugated verb follows directly.
Im Wesentlichen geht es um eine finanzielle Frage.
Essentially, it's about a financial question.
As an adjective, 'wesentlich' (essential) is often combined with abstract nouns to emphasize their importance. Typical examples are: 'ein wesentlicher Unterschied' (an essential difference), 'ein wesentlicher Beitrag' (an essential contribution), 'ein wesentlicher Aspekt' (an essential aspect), 'ein wesentlicher Grund' (an essential reason).
Er hat einen wesentlichen Beitrag zum Erfolg des Teams geleistet.
He made an essential contribution to the team's success.
important
Wichtig and wesentlich both describe something of great importance. Wichtig is the more general assessment. Wesentlich emphasizes more strongly that something is fundamental, decisive, or a necessary core component of the whole.

Eine gesicherte Finanzierung ist für die Durchführung des Projekts wesentlich.
Secured funding is essential to carrying out the project.
Eine klare Zeitplanung ist für das Projekt wichtig.
A clear schedule is important for the project.