Cousin is a term bandied about with sublime disregard for precision. This is particularly the case among internet-using family historians: any distant relative who pops up out of the ether is immediately given the epithet 'cousin', no matter what the actual degree of relationship. Such assumptions can produce tricky situations.
A person's first cousin (or cousin german) is the child of an uncle or aunt. That seems fairly straightforward, except that to be accurate the 'uncle' and the 'aunt' must be the person's parent's brother or sister - not merely someone who has been called 'uncle' or 'aunt' yet isn't a blood relative. This presents a problem if you've grown up, as I did, being told to call a large number of adults 'uncle' or 'aunt', many of whom were simply close friends of my parents. Our neighbours - a childless couple who took an interest in me - were naturally 'uncle' and 'aunt', and remained so to me until their deaths by which time I was a married woman with children of my own.
My paternal grandmother had a whole raft of sisters who should have been regarded as my 'great-aunts' (grand-aunt being the old-fashioned form) but who much preferred me to call them 'aunt'. A real aunt's husband may be called uncle, but he isn't a blood relative, just an 'in-law'. This is not always explained to the younger generation who can't be blamed for the resulting confusion.
Perhaps most people don't much care one way or the other, though these perceived relationships can plunge family historians into deep trouble. It's vital to know the distinction between a first cousin twice removed and a third cousin. The term twice removed indicates a difference of two generations - once removed a difference of one generation, and so on. Second cousins are the grandchildren of a person's grandparents' siblings. Er - yes, I think that's right.
The habit of calling people 'Cousin Helen' etc died out some time ago, which is probably just as well. During my childhood it simply wasn't the done thing for a schoolgirl to call her aunts and uncles by their first names. The current trend is for a child to call almost anyone by their first name - not excluding its own parent.
There are several charts available online to help with working out complex relationships while you're compiling the family tree, for example: