I am currently reading Martin Fowler\'s UML Distilled. I have just covered the section on class diagrams, where he places strong emphasis on the need to sort out ones perspectiv
Here's how I explain the ideas to developers.
Conceptual is the relationships. This is the level where coupling should happen. You shouldn't see coupling from conceptual to implementation - that's a signal of a poor design.
Specification defines the algorithm without defining the implementation. In a class diagram, this might be represented as an abstract class. Alan Shalloway calls methods which fall into this realm "Sergeant methods": They just bark orders.
Implementation is where the actual work happens. This might be represented by concrete classes which implement your abstract specifications.