Not sure if this qualifies as putting it in 'simple terms' but here goes...
The nth cousin of a person shares a common ancestor n+1 generations away. For example, First cousins share an ancestor 2 generations away (i.e. a grandparent). In most cases it is simpler to just use n-1 to determine the number of "greats" to put in front of "grandparent" - for example 3rd cousins share a (3-1=) 2nd great-grandparent.
When we say people are 'removed' it indicates that the two people do not have the same relationship to the shared pair of ancestors. The 'number of time removed' indicates the number of generations that separate the two individuals. For the sake of illustration let's consider "zeroth cousins" which have special names that we are much more familiar with - a 0th cousin we would normally call a brother or sister and a "0th cousin once removed" would be a niece or nephew, a grand niece/nephew (interchangeably called a great-niece/nephew) would be a "0th cousin twice removed", and so on. In the case of the 0th cousin once removed (i.e. niece/nephew) the shared ancestor is one person's parent (0th cousin+1 = 1 generation away from the shared ancestor), and the other person's grandparent (The first person is 1 generation from shared ancestor + 1 times removed = the second person is 2 generations from the shared ancestor).
Pulling this all together to answer your question when a relationship is "3rd cousin 6 times removed" what we are saying is one person is (3+1=) 4 generations removed from the shared ancestor and the other person is (4+6=) 10 generations removed - or if we want to put it another way one person is the (3-1=) 2nd great-grandchild of the shared ancestor, and the other person is the (2+6=) 8th great-grandchild of the shared ancestor.
Note: you may also see "half-cousin" relationships mentioned - this label can be useful in some cases, but as far as I am aware it is not a "generally accepted practice".
