Psychological core is what people often call the 'real you' and is the part of you that contains your beliefs, values, attitudes and interests and all of these are relatively constant. 

Typical responses are the way that you act to the world around you and with different situations you will act differently. For example if you get fouled in football you may shout and make a fuss but then if you are meeting new people you may be quiet and shy because you don't want to overwhelm them or come across the wrong way so you change the way you are around people because your environment has changed. These are often good indicators of your psychological core.