Here's a perfect example:
One night we came home from dinner and noticed that our outdoor cat, Billy, had white feathers all over his black fur. We didn't know what to make of it till we got to the font door. There were bird feathers all over the steps. What conclusions can you draw from these limited facts?
1. The cat caught a bird.
2. The cat killed a bird.
3. The cat found a down pillow and tore it to shreds.
Wait! I have to tell you there was no evidence of any blood. Nor was there evidence of a dead bird anywhere.
So, how can you reach the conclusions above without seeing what really happened and without any witnesses? Using circumstantial evidence.
We know cats chase birds.
We know that cats will kill birds if they can catch them.
We know that cats typically don't walk around with bird feathers all over them.
We know that birds don't naturally implode and leave their feathers all over our front steps.
Therefore, if we were a prosecutor, we could argue that there's a logical sequence of what happened and the only conclusion is that our beautiful outdoor cat killed a bird. A defense attorney would argue that since there's no direct evidence of blood or a body, then you cannot conclude that the cat killed a bird.
That, in a nutshell, is circumstantial evidence.