The phrase employs delenda, the feminine singular gerundive form of the verb dēlēre (“to destroy”). The gerundive (or future passive participle) delenda is a verbal adjective that may be translated as “to be destroyed”. When combined with a form of the verb esse (“to be”), it adds an element of compulsion or necessity, yielding “is to be destroyed”, or, as it is more commonly rendered, “must be destroyed”. The gerundive delenda functions as a predicative adjective in this construction, which is known as the passive periphrastic.
The short form of the phrase, Carthago delenda est, is an independent clause. Consequently, the feminine singular subject noun Carthago appears in the nominative case. The verb est[i] functions as a copula—linking the subject noun Carthago to the predicative verbal adjective delenda—and further imports a deontic modality to the clause as a whole. Because delenda is a predicative adjective in relation to the subject noun Carthago, it takes the same number (singular), gender (feminine) and case (nominative) as Carthago.
The fuller forms Ceterum censeo delendam esse Carthaginem and Ceterum autem censeo delendam esse Carthaginem use the so-called accusative and infinitive construction for the indirect statement. In each of these forms, the verb censeo (“I opine”) sets up the indirect statement delendam esse Carthaginem (“[that] Carthage is to be destroyed”). Carthaginem, the subject of the indirect statement, is in the accusative case; while the verb esse is in its present infinitive form. Delendam is a predicate adjective in relation to the subject noun Carthaginem and thus takes the same number (singular); gender (feminine); and case (accusative) as Carthaginem.
Now you decide. Did someone think this was a necessary and useful addition to the article? Or did it occur to some Wikipedia editor that it would be an amusing jab at Wikipedians’ notorious pedantry to spin three fairly long paragraphs of “grammatical analysis” out of three words in Latin?