Format "annotation" field in biblatex

Biber parses all new-line characters into normal spaces (as does BibTeX, I think), so you can't get a new paragraph with a blank line in the .bib file. par seems the simplest option.

But I would say that the .bib file might simply not be the best place to write long annotations about your entries.

If you want to add larger annotations to your .bib entries it might be more convenient to use an external .tex file to store these annotations (where you can use blank lines for par). See also How to embed a review in biblatex?, §3.13.8 External Abstracts and Annotations and §4.11.3 External Abstracts and Annotations of the biblatex manual.

documentclass[british]{article}
usepackage[T1]{fontenc}
usepackage[utf8]{inputenc}
usepackage{babel}
usepackage{csquotes}

usepackage[style=authoryear, loadfiles, backend=biber]{biblatex}

renewbibmacro{finentry}{%
  setunit{%
    finentrypunct
    renewcommand*{finentry}{}%
    par}%
  usebibmacro{annotation}%
  finentry
}

begin{filecontents}{jobname.bib}
@book{appleby,
  author     = {Humphrey Appleby},
  title      = {On the Importance of the Civil Service},
  date       = {1980},
}
end{filecontents}
begin{filecontents}{bibannotation-appleby.tex}
Lorem ipsum [x^2+y^2=z^2] that was mathy.
Also $a+b=c$ and so forth.
Just a few words to make the next
paragraph stand out properly.

We can even have a new paragraph.
end{filecontents}

addbibresource{jobname.bib}
addbibresource{biblatex-examples.bib}


begin{document}
cite{sigfridsson,appleby}
printbibliography
end{document}

---

For a heavier paragraph markup you can either customise

setlength{bibparsep}{0.5baselineskip plus 2pt}

or just change the paragraph settings before you print annotation (normally you would probably not set both parskip and parindent to non-zero values, but this is just for demonstration purposes)

renewbibmacro{finentry}{%
  setunit{%
    finentrypunct
    renewcommand*{finentry}{}%
    par}%
  setlength{parskip}{0.5baselineskip plus 2pt}%
  setlength{parindent}{1em}%
  usebibmacro{annotation}%
  finentry
}

(I'm not too fond of having formatting settings like this just in a bibmacro, but that was the easiest way to get them right since they act on paragraphs.)