Since this question seems to be kind of popular, let me add another answer.
In general you should not update
biblatex or Biber manually. Use your TeX distribution (MikTeX and its Console or TeX live and its
tlmgr: How do I update my TeX distribution?) to install and update packages.
The problem with manual updates is not only that the versions of
biblatex and Biber need to match exactly, but also that
biblatex has (admittedly milder) dependencies on other packages as well (which in turn may have dependencies themselves). So you can never be sure that you only need to update
biblatex and Biber, you may as well have to update
xstring and a few other packages. Vice versa packages that depend on
biblatex may also have to be updated. This can mean that you need to update many more packages than just
biblatex and Biber.
If you let your TeX distribution sort that out for you, your chances of getting package versions that actually work together are much higher.
If your TeX distribution does not offer updates any more (vanilla TeX live is frozen each year, see Why does TeX Live "require" yearly updates? and the TeX live that ships in the repositories of many Linux distributions is frozen and often already a few months behind at release), you should think about updating your TeX distribution as a whole. If you want to get the newest updates on Linux machines with TeX live in the software repositories you may need to install "vanilla" TeX live: How to install "vanilla" TeXLive on Debian or Ubuntu?.
The advantage of upgrading to a new TeX live is that old installations can usually coexist with the new one, so you have a back-up system should something be wrong.
So to reiterate: Do not update
biblatex or Biber manually.
In case you absolutely must update the two packages manually, prepare to have to update many other packages as well. Usually you should get meaningful errors or warnings that can give you hints about which packages need updating, but you can never be sure (some lower level
etoolbox changes for example can yield cryptic error messages that don't really point at
etoolbox, e.g. biblatex broken overnight).
Check the compatibility matrix in the
biblatex or Biber manual for matching versions of
biblatex and Biber. Choose the one you want (probably either the newest or a specific version combination for arXiv).
Get the corresponding versions from SourceForge.
If you want the newest version you can also refer to CTAN: https://www.ctan.org/pkg/biblatex and https://www.ctan.org/pkg/biber
Decide whether you want to replace the system files that are already installed with your version or whether you want to install your versions in a local tree where they are given precedence over the system files (see also https://texfaq.org/FAQ-inst-wlcf). Usually the second option is the saner one and people discourage you from going for the first.
Follow How do I install an individual package on a Linux system? or https://tex.stackexchange.com/q/405142/35864 to install
Extract the Biber executable into the proper place. (Either overwriting the existing executable - which is not advised - or install into
/usr/local/bin or a subdirectory of
/home with appropriate path settings).