Heat is the total kinetic energy of all the particles in a given system. Heat is thermal energy that always spontaneously flows from a region of higher temperature to one of lower temperature. Remember "total of all" for heat. A good way to think of the concept of the "total of all" is to imagine that you wanted to measure the height of students in your class. One way to do it would be to have each student stand on the head of another student and so on stacking the students on top of each other. Ouch! Not only would you most likely have to cut a hole in the roof, but you'd need a very long measuring device to get the students' heights. This would give you the "total height of all" students. Heat is the "total kinetic energy of all" particles.
What is conduction?
Conduction is the transfer of heat from one substance to another substance. The particles of the two substances must be in direct contact for conduction to occur. For example, if a person grabs a hot pan, the pan's particles come in direct contact with the person's hand and heat passes from the pan to the hand. Since the pan is at a higher temperature than the hand, the pan's particles vibrate more vigorously. The pan's particles transfer some of the increased motion to the particles of the hand, causing the hand's particle to vibrate more. This increased vibration of the hand's particles is what we detect as something feeling hot.
What is insulation?
Substances that don't conduct heat very well are called insulators. Since every material can have its particles vibrate more if they contact another material whose particles are vibrating vigorously, all materials do conduct some heat. A good insulator however transfers only a small amount of this increased motion throughout its particles. Small changes in the motion of the particles of a substance means that the temperature of the substance will not change very much when the material is exposed to different temperatures.
What is thermal conductivity
Thermal conductivity is the amount of heat energy transferred by a material if exposed to a source of heat. A substance with a high thermal conductivity transfers more energy than a substance with a low thermal conductivity. Iron metal transfers heat over 100 times better than water. So iron would have a high thermal conductivity while water would have a relatively low conductivity.

Table of Thermal Conductivity