There are two main reasons why this does not work out of the box as intended.
As mentioned by Paul Stanley in the comments the field groups is not a standard field and therefore not recognised by Biber. That means that the contents of the field groups don't make it to the .bbl file, which in turn means that biblatex can not access its contents.
You would have to declare the groups field as shown in Add field "tome" to biblatex entries
Secondly, and more seriously, with \iffieldequalstr{<field>}{<string>} you only compare the (entire) contents of the field <field> to the string <string>. That means that \iffieldequalstr{groups}{Group1} yields false when groups is groups = {Group1,Group2},. This is also alluded to in Paul Stanley's comment.
Like gusbrs and Paul Stanley I recommend you look into keywords as that field was intended to filter entries into groups.
\documentclass{article}
\usepackage[style=authoryear,backend=biber]{biblatex}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@misc{A01,
author = {Author, A.},
year = {2001},
title = {Alpha},
keywords = {Group1,Group2},
}
@misc{B02,
author = {Buthor, B.},
year = {2002},
title = {Bravo},
keywords = {Group1},
}
@misc{C03,
author = {Cuthor, C.},
year = {2003},
title = {Charlie},
keywords = {Group2},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\nocite{*}
\printbibliography[keyword=Group1]
\end{document}
If you have already populated hundreds of entries with groups instead of keywords you can use Biber to remap the fields.
\DeclareSourcemap{
\maps[datatype=bibtex]{
\map[overwrite]{
\step[fieldsource=groups, final]
\step[fieldset=keywords, fieldvalue={,}, append]
\step[fieldset=keywords, origfieldval, append]
\step[fieldsource=keywords, match=\regexp{\A,}, replace={}]
}
}
}
edit This now uses gusbrs' method from \DeclareSourceMap does not work to avoid a leading comma without an item.
If for some reason you are wedded to the idea of a groups field and don't want to involve keywords at all, here is a crude implementation of a test that loops over a field with comma-separated values and checks if Group1 is contained as list element in the groups field.
\documentclass{article}
\usepackage{filecontents}
% make the groups field known to biblatex
\begin{filecontents*}{groups.dbx}
\DeclareDatamodelFields[type=field,datatype=literal]{groups}
\DeclareDatamodelEntryfields{groups}
\end{filecontents*}
\usepackage[style=authoryear,backend=biber,datamodel=groups]{biblatex}
% traverse the groups field to find a match
\makeatletter
\newtoggle{bastianblx@isgroup}
\newcommand*{\bastianblx@ifmatch}[2]{%
\ifstrequal{#1}{#2}
{\toggletrue{bastianblx@isgroup}\listbreak}
{}}
% switch the order of the arguments for easier \expandafter work
\newcommand*{\bastian@forcsvlist}[2]{%
\forcsvlist{#2}{#1}}
\defbibcheck{Group1}{%
\togglefalse{bastianblx@isgroup}%
% 31 \expandafters for five levels of expansion
\expandafter\expandafter\expandafter\expandafter\expandafter
\expandafter\expandafter\expandafter\expandafter\expandafter
\expandafter\expandafter\expandafter\expandafter\expandafter
\expandafter\expandafter\expandafter\expandafter\expandafter
\expandafter\expandafter\expandafter\expandafter\expandafter
\expandafter\expandafter\expandafter\expandafter\expandafter
\expandafter
\bastian@forcsvlist
\expandafter\expandafter\expandafter\expandafter\expandafter
\expandafter\expandafter\expandafter\expandafter\expandafter
\expandafter\expandafter\expandafter\expandafter\expandafter
\expandafter\expandafter\expandafter\expandafter\expandafter
\expandafter\expandafter\expandafter\expandafter\expandafter
\expandafter\expandafter\expandafter\expandafter\expandafter
\expandafter
{\thefield{groups}}{\bastianblx@ifmatch{Group1}}%
\iftoggle{bastianblx@isgroup}{}{\skipentry}%
}
\makeatother
\begin{filecontents}{\jobname.bib}
@misc{A01,
author = {Author, A.},
year = {2001},
title = {Alpha},
groups = {Group1,Group2},
}
@misc{B02,
author = {Buthor, B.},
year = {2002},
title = {Bravo},
groups = {Group1},
}
@misc{C03,
author = {Cuthor, C.},
year = {2003},
title = {Charlie},
groups = {Group2},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\nocite{*}
\printbibliography[check=Group1]
\end{document}
All solutions show

keywordto filter? I'm afraid I don't have time this morning to fiddle. – Paul Stanley Jan 28 '19 at 12:06keywords, except if there are unstated special requirements. – gusbrs Jan 28 '19 at 12:15groupshas been introduced by JabRef to allow for explicit grouping of entries: https://docs.jabref.org/finding-sorting-and-cleaning-entries/groups - The development team decided against a reuse of "keywords" as there was a strong opinion to keep "keywords" as specified by the author of the paper. Thus, they must not be modified. – koppor Jul 23 '22 at 18:57