A pseudo class describes a state or a position rather than a thing you marked: hover, focus, first child, every other row. They are the way to style states without adding markup, and the way to write selectors that are hard to read.
About 1 min of reading
Give a link all its states.
Hover only
Before you run it, say out loud what it will print. Then open the answer.
Add focus
Before you run it, say out loud what it will print. Then open the answer.
A page where only hover changes the look has no visible keyboard state. Styling focus is a two line rule that fixes a real accessibility failure, and it is the one that is checked most often.
Content generated by CSS is not in the HTML, so a reader, a search, and a copy of the page do not see it. Put real words in HTML and use generated content for marks and decoration.
hover, active, and focus style the same element in different situations. A link needs all three, and a control that only has hover is a control that cannot be seen as selected with a keyboard.
first-child, last-child, and nth-child select by position. That is how a table row can stripe without a class per row, and how a list can drop the margin on its last item.
before and after insert content you did not write in HTML. Useful for decoration, and a trap for meaning: text generated in CSS is not part of the document in the way a reader expects.
Each one is defined here on this site. Open the entry for the full definition and the other words it points at.