begin{explanation}
Here starts the explanation ...
 end{explanation}

documentclass[10pt,a4paper]{article}
usepackage[latin1]{inputenc}
usepackage{amsmath}
usepackage{amsfonts}
usepackage{amssymb}
usepackage{graphicx}
newenvironment{explanation}{textbf{Explanation.} }{}
begin{document}
end{document}