"Sentir bon" vs "Se sentir bien" - The different meanings of the verb "sentir" in French

The verb sentir and its reflexive form se sentir are used in a broad sense to express physical or emotional feelings (e.g. to smell good / to feel good).

Using "sentir" and "se sentir" in French

- sentir bon / mauvais  (physical)

This means to smell good / bad.

Note that, in the specific case of sentir, even though bon and mauvais are adjectives, these are fixed expressions, so bon and mauvais NEVER change (no agreement).

- se sentir bien / mal / mieux ... (emotional)

(literally to feel oneself)  It means to feel good / well / fine / bad / better.

In this context, se sentir is identical in meaning to aller. See Expressing how you are with aller (Greetings in French). 

e.g.  Je vais bien.  /  Je me sens bien.

Se sentir can also be used with adjectives to express someone's impression of how they are, how they feel. 

See also Describing senses with "sentir" - The different meanings of the verb "sentir" in French