The problem occurs because of the subtle length-management when using a minipage within a minipage. The outer minipage of width 0.48\linewidth sets the line width within that minipage to 0.48\linewidth. If the inner minipage is set to a width of 0.48\linewidth, it is actually 0.2304 of the original \linewidth, since the nested minipage compounds the lengths. You also need to remove the spurious space after \fbox{ by using %. Using this is better:
\documentclass{article}
\usepackage{caption,subcaption}%
\usepackage{calc}% http://ctan.org/pkg/calc
\usepackage[showframe]{geometry}% http://ctan.org/pkg/geometry
\begin{document}
\noindent\begin{minipage}[t]{0.48\linewidth}%
\centering
\fbox{%
\begin{minipage}[t]{\linewidth-2\fboxsep-2\fboxrule}% Remove fbox rule/sep width
picture1
\end{minipage}}
\captionof{figure}{picture1}\label{fig:picture1}
\end{minipage}\hfill
\begin{minipage}[t]{0.48\linewidth}%
\centering
\fbox{%
\begin{minipage}[t]{\linewidth-2\fboxsep-2\fboxrule}% Remove fbox rule/sep width
picture2
\end{minipage}}
\captionof{figure}{picture2}\label{fig:picture2}
\end{minipage}
\end{document}

If you're interested in a vertical divider between the two images to visually separate them from one another, one could typeset the entire structure inside a multicols environment:
\documentclass{article}
\usepackage{caption,subcaption}%
\usepackage{calc}% http://ctan.org/pkg/calc
\usepackage{multicol}% http://ctan.org/pkg/multicol
\usepackage{lipsum}% http://ctan.org/pkg/lipsum
\begin{document}
\lipsum[1]
\renewcommand{\columnseprule}{0.4pt}% Columns are separated by rule of width 0.4pt
\begin{multicols}{2}% Two-column layout
\setlength{\parindent}{0pt}% No paragraph indent
\begin{minipage}[t]{\linewidth}%
\fbox{%
\begin{minipage}[t]{\linewidth-2\fboxsep-2\fboxrule}% Remove fbox rule/sep width
picture1
\end{minipage}}
\captionof{figure}{picture1}\label{fig:picture1}
\end{minipage}
\begin{minipage}[t]{\linewidth}%
\fbox{%
\begin{minipage}[t]{\linewidth-2\fboxsep-2\fboxrule}% Remove fbox rule/sep width
picture2
\end{minipage}}
\captionof{figure}{picture2}\label{fig:picture2}
\end{minipage}
\end{multicols}
\lipsum[2]
\end{document}

The use of the calc package is merely for calculation of lengths. And, the geometry package is used to highlight the page frame. Also, the lipsum package provides some dummy text.