State verbs express states or conditions which are relatively static. They include verbs of perception, cognition, the senses, emotion and state of being:
like
love
own
understand
want
remember
believe
belong, etc.
Such kind of verbs are not used in the Continuous Tenses, because they describe rather state than an action.
Wrong:
I am not understanding you.
She is wanting this apple.
They are believing me.
Right:
I don't understand you.
She wants this apple.
I believe you.
Activity verbs (also called dynamic verbs or action verbs) express activities, processes, momentary actions or physical conditions:
dance
cook
watch
throw
help
eat, etc.
They may be used in continuous forms:
Are you dancing with her?
My father is cooking lunch.
I was eating meat.
Some verbs may be used as states and activities both, which depends on the context. Let us compare some situations:
You look great in those jeans. (look=appear, state)
What are you looking at? (look=watch, activity)
I have a dog. (have=possess, state)
I am having my lunch now. (have=eat, activity)
I think, you are wrong. (think=believe, state)
I am thinking of getting away from here (think=consider, activity)
I feel, the article is agressive. (feel=believe, state)
Are you feeling tired? (feel=experience a feeling, activity)
The cooking smells nice (smell=to have an odour, activity)
Why are you smelling this soup? (smell=to test by one's nose, activity)