Though in his lectures, Feynman didn't define [conservation law](http://en.wikipedia.org/wiki/Conservation_law), he did use it while explaining divergence theorem:

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> [...] heat is **conserved**. That is, no heat is generated inside the material and the amount that decreases inside equals the amount that goes outside [...] So, in circumstances in which heat would be conserved , we say that $$\int\_s \mathbf{h} \cdot \mathbf{n} da = -\dfrac{dQ}{dt}.$$
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Now, what is new in it? If something goes outside, then it will decrease inside! I can understand the equation but unable to concieve what really is "conservation-law".

While reading the wikipedia, other sites, some answers to my question here, I got to know that conservation deals with those stuff that doesn't appear to any other place, doesn't get destroyed, etc, etc. . . 

What is the meaning of "conservation" actually ? And also, why is the equation termed as **continuity** equation ? What is meanty by "continuity"?