Heuristic values
These are the values give to each node in relation to the goal. A simple example would be distance. If each city is a node, the heuristic values of a node can be the straight line between this city node and the goal city node. This value is a measurement on top of the path values in a graph.
Admissiblity
An admissble heuristics is a heuristics that never over estimates the true cost to the goal states. It estimate a number that is below the true cost.
Consistency
A consistent heuristics is a heuristics that adds up. Meaning that the forming of a heuristics value is based on previous heuristics. B node's heuristics value will be A nodes' heuristics value plus the path value between A and B.