Sentences
是 joins nouns, and adjectives do not need it
是 means am, is and are, but only between two nouns. Adjectives work like verbs and take 很 instead.
是, shì, links a subject to a noun: I am a teacher, this is tea. It is not used with adjectives, because a Chinese adjective already contains the idea of to be. 忙, máng, means busy and also is busy. A bare adjective sounds like the start of a comparison, so a plain description takes 很, hěn, in front, which in that position means little more than is.
Examples
我是老师wǒ shì lǎoshīI am a teachertwo nouns, so 是
这是茶zhè shì cháthis is tea
我很忙wǒ hěn mángI am busy很, and no 是
今天很热jīntiān hěn rèit is hot today
Watch out
The mistake this causes
Saying 我是忙 for I am busy. Adjectives take 很, never 是.