wichtig
important
Being of great importance, relevance, or significance.
Es ist wichtig, dass du pünktlich zum Termin kommst.
It is important that you arrive on time for the appointment.

important
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important
Being of great importance, relevance, or significance.
Es ist wichtig, dass du pünktlich zum Termin kommst.
It is important that you arrive on time for the appointment.

'Wichtig' is very often used in the impersonal constructions 'Es ist wichtig, dass…' (It is important that...) with a subordinate clause, or 'Es ist wichtig, … zu…' (It is important to...) with an infinitive, to express a necessity.
Es ist wichtig, die Anweisungen genau zu lesen.
It is important to read the instructions carefully.
To express for whom something is important, German uses the verb 'sein' (to be) with the dative. The person is in the dative, and the important thing is the subject.
Meine Familie ist mir sehr wichtig.
My family is very important to me.
The reflexive expression 'sich wichtig machen' (to act important) is a fixed idiom. It has a negative meaning and describes someone who shows off and presents themselves as more important than they are.
Er versucht immer, sich vor dem Chef wichtig zu machen.
He always tries to act important in front of the boss.
big / great
'groß' and 'wichtig' can both express that something has a lot of significance. 'wichtig' says directly that something is relevant and must be taken into account. In this sense, 'groß' sounds more like 'significant' or 'with major consequences', for example in 'eine große Entscheidung' (a big decision) or 'ein großer Erfolg' (a great success). Learners may confuse the words because 'groß' can mean not only size, but also significance. If you want to clearly say that something plays a role or is necessary, 'wichtig' is usually more precise.

Vor der Reise ist ein gültiger Ausweis besonders wichtig.
Before the trip, a valid ID is especially important.
Der Umzug in eine andere Stadt ist für Mara ein großer Schritt.
Moving to another city is a big step for Mara.