I do not really understand, what you are trying, but the first argument of \ifthenelse should surely be a comparison, maybe something like:
\documentclass{article}
\usepackage{ifthen}
\usepackage{currfile}
\newcommand{\textforpicture}[1]{%
\ifthenelse{\equal{#1}{John}}
{This is text 1 and the name of this file is \currfilebase}%
{\ifthenelse{\equal{#1}{Jack}}
{This is text 2 and the name of this file is \currfilebase}%
{\ifthenelse{\equal{#1}{Jill}}
{This is text 3 and the name of this file is \currfilebase}
{nothing}
}%
}%
}%
\begin{document}
Experimental text fragement for John: \textforpicture{John}
Experimental text fragement for Jack: \textforpicture{Jack}
Experimental text fragement for Jill: \textforpicture{Jill}
\end{document}
For such cases, you can also use l3:
\documentclass{article}
\ExplSyntaxOn
\newcommand%\newcommand{\textforpicture}[1][1]% could be used, but using
\NewDocumentCommand \textforpicture { m } % is usual for defining a user command in l3 context.
{
\str_case:nnF { #1 }
{
{John} {This~is~text~1}
{Jack} {This~is~text~2}
{Jill} {This~is~text~3}
}
{nothing}
}%
\ExplSyntaxOff
\begin{document}
Experimental text fragement for John: \textforpicture{John}
Experimental text fragement for Jack: \textforpicture{Jack}
Experimental text fragement for Jill: \textforpicture{Jill}
\end{document}
I've removed currfile in this second example, because I've not understood, why you are using it. And IMHO it is also not needed to show, how to use \str_case:nnF.
Please have a look into “The LaTeX3 interfaces” for more information about using LaTeX3.