Hands up if you have no idea what "1st cousin, once removed" means. Hands up again if you call the children of your first cousins your second cousins.
One of the hardest things about beginning one's genealogical journey is having to learn an entirely new language. There are relatives once, twice, three times removed. There are census abbreviations that make no sense whatsoever. There are occupation titles no one in the last century has encountered. There are centimorgans and haplogroups. There are words like "generation" and "cousin" that are used differently in genealogy than in common conversation. Discovering your ancestral history means also discovering a brand new collection of words, terms, titles, and definitions. And few are as frustrating to figure out than the broad assortment of cousins.
In order to figure out these familial designations, it's important to understand two things first: one, "cousin" does not just refer to the children of your parents' siblings, as we most often use it. A cousin is anyone with whom you share a common ancestor who is not your sibling, parent, child, aunt/uncle, or niece/nephew. Two, "generation" in genealogical terms does not refer to people born in the same time-frame (we're not talking Gen X or Millennials, here), it refers to how one fits into their family tree. Despite the fact that there is a 30 year difference between my youngest and oldest first cousin, we are all part of the same generation, as we all descend from the same generation - our parents and their siblings.
With that understood, figuring out what type of cousin someone is to you becomes considerably easier. We already know that "cousin" refers to someone with whom you share a common ancestor. What type of cousin they are is decided by how you each relate to that common ancestor. First cousins share a common grandparent. You are the generation born to your parents and their siblings. First cousins once removed, then, are people who share an ancestor, but are separated by a generation - your grandparent is their great-grandparent, or vice versa. This can apply to your parents' first cousins, or the children of your first cousins. But wait! Most of us grew up calling the children of our first cousins our second cousins. That's clearly not accurate, so...who are our second cousins? Second cousins, like first cousins, are part of the same generation, only instead of sharing a grandparent, we share a great-grandparent. Or, put another way, our parents aren't siblings, our grandparents are.
Still confused? Let's break it down a little more.
First cousins=shared grandparent
Second cousins=shared great-grandparent
Third cousins=shared great-great-grandparent
First cousin, once removed=my grandparent is their great-grandparent, or vice versa
First cousin, twice removed=my grandparent is their great-great-grandparent, or vice versa
Second cousin, once removed=my great-grandparent is their great-great-grandparent or vice versa
Second cousin, twice removed=my great-grandparent is their great-great-great-grandparent, or vice versa
It all seems very confusing, I know, and no matter how many people explain it in their own well-meaning way, it's likely going to take you figuring out your own system to best remember these various designations. Focusing on the genealogical meanings of "cousin" and "generation" is simply what worked best for me.
Good luck, and happy hunting!