So there are three forms of the imperative: one for "du," one for "ihr," and one for "Sie."
Du: "Zeige mir die Welt" (we can also drop the "-e" here: "Zeig"; either form works for most verbs, but for some verbs one or the other may be more common; so, yeah, this is the same as dropping the "-(e)n" from the infinitive form)
Ihr: "Zeigt mir die Welt" (same as the normal indicative "ihr" form, and not just dropping the "-(e)n")
Sie: "Zeigen Sie mir die Welt" (this has the subject ("Sie") here, which we do not use in the "du" and "ihr" forms)
The sentence is 'Show me the world.' Some verbs use a Dative pronoun and zeigen is one of those verbs for the 'show me' part of the sentence. So, 'show me' = 'zeige mir' (and not mich). 'The World' in this case is the direct object so it would be akkusativ/accusative case, which is why it is 'die Welt' and not 'der Welt.' The dative portion of the sentence only impacts zeigen and not die Welt.