Let's start with the basics.
This is Bob.
We'll use him to show different relationships with his family.
Bob's immediate family consists of his brother, his sister, and his parents.
We can make this a whole lot simpler by just showing one of Bob's parents.
This now represents Bob's mom or dad.
We'll do the same thing for his siblings.
At some point, Bob's sibling may decide to have a child of their own.
This person would be Bob's nibbling.
...or more commonly known as niece or nephew.
At some point Bob's niece or nephew may also have a child.
This person would be Bob's grand niece or nephew.
...and the next generation would be great grand.
With each generation after this you just add another "great" on it.
Now let's expand this above and little bit.
Bob's parent also has a parent which would be Bob's grandparent.
The have another child beside's Bob's parent:
This is Bob's aunt or uncle.
Any child here is Bob's first cousin - you and I might just say cousin.
Notice that first cousins share the same grandparents.
In other words cousins are children of siblings.
Here's where it gets a little interesting:
If Bob's cousin decides to have a child, this child will be Bob's first cousin once removed.
The "once removed" part refers to them being one generation apart.
To find a common ancestor, Bob has to go up two generations.
...and his first cousin once removed has to go up three generations.
So, if we continue this pattern downwards:
This would be Bob's first cousin twice removed, and so on...
Continuing upward, here's Bob's great grandparent.
And here's Bob's grand aunt or uncle.
A child here is once again Bob's first cousin once removed.
Bob has to go up three generations and his cousin only has to go up two generations.
And down one more level, here's Bob's second cousin.
Notice that second cousins share the same great grandparent.
Just as we did with Bob's first cousin,
this is Bob's second cousin once removed,
and so on...
We could expand this out again:
great great grandparent,
great grand aunt or uncle,
first cousin twice removed,
second cousin once removed,
and third cousin.
Below Bob's generation, things are simple:
just keep adding one to the removed part.
third cousins once removed, third cousins twice removed,
and so on...
Let's take a good look at what we have so far.
We can expand Bobs family tree as far as we want.
However, unless Bob is an avid genealogist,
he probably doesn't know much past his grandparents.
Bob probably only knows and keeps in contact with a few of his cousins.
At some point, cousins up here
probably aren't alive anymore.
and cousins down here haven't been born yet.
but many cousins out here are probably alive and well
Bob just doesn't know who they are...