Why are these lines in my references not breaking?

You'll find that those lines that don't break properly are those that are underlined. Indeed, underlining is quite hard in LaTeX: In standard LaTeX \underline does not allow line breaks (https://texfaq.org/FAQ-underline). There are alternative packages like soul and ulem that allow for a more sophisticated underlining mechanism, but their implementations also have limitations and usually only work smoothly for very simple input that does not feature too many macros. Fortunately, underlining is usually frowned upon in typography as a relic of the typewriter age and so LaTeX can get away with not supporting it as well as other word processors do.

If you know the output the biblatex standard styles, you'll find that the text that is underlined in your screenshot is usually printed in italics.

Putting that together suggests that you are loading the package ulem, whose default behaviour it is to redefine \em and \emph to produce underlined text instead of the normal italics.

The following MWE reproduces the effect you are seeing in your screenshot

\documentclass[british]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{babel} \usepackage{csquotes} \usepackage{ulem} \usepackage[style=authoryear, backend=biber]{biblatex} \addbibresource{biblatex-examples.bib} \begin{document} \cite{sigfridsson} \printbibliography \end{document} 

As explained in Getting \emph back to normal after loading ulem you can load the package ulem with the option normalem to avoid \emph being redefined. And indeed with

\usepackage[normalem]{ulem} 

instead of \usepackage{ulem} the code produces

Of course you can also stop loading ulem completely if you don't need underlining in your document.