Stative (or state) verbs describe states (things that don't change easily or quickly, for example, what you believe, think or own) rather than actions (jump, talk or buy). These verbs are not normally used in the continuous form (ing).
Stative verbs can be grouped into these categories:
Verbs of emotion:
care feel hate like loathe love need prefer want
Verbs of ownership:
own have possess
Verbs of the mind:
believe mean suppose forget realise understand know remember doubt
Verbs of the senses - often used with 'can':
hear see smell taste touch
contain depend matter
Some of these stative verbs can be used in the continuous form but their meaning will change. For example:
Do you think so? (Stative - Is that your opinion? Is that the state of your belief?)
He's thinking about his friends in Poland (Dynamic - The action of thinking. His friends are in his thoughts, in his mind right now but he might be thinking of something else soon).
He has got brown eyes (Stative - He possesses brown eyes. The colour is unlikely to change).
He's having a pint of beer (Dynamic - The action of drinking. He might be drinking something else soon).
I don't see what you mean. (Stative - I don't understand what you mean).
She is seeing him next week. (Dynamic - She is meeting him).