是 shì is a special verb, called a copula. It links two noun phrases with the second noun phrase characterising or identifying
the initial noun phrase.
For example:
我是学生。 Wǒ shì xuésheng. I am a student.
王先生是老师。 Wáng xiānsheng shì lǎoshī. Mr Wang is a teacher.
是 can also be used to give an affermative answer to questions of the form 'Is X Y?'.
你是学生吗? Nǐ shì xuēsheng ma? Are you a student?
是。 Shì. Yes.
Note that predicative adjectives do not require the use of 是.
To ask somebody if they are well, you would say 你好吗? not *你是好吗?
Similarly: 他老,我小。 Tā lǎo, wǒ xiǎo. He is old, I am young.
The adjectives 老 and 小 can function as verbs; unlike adjectives in English that require a copula.