This is a standard feature. At the beginnings, most of the fixed tags were harcoded into lplain.tex, the main file for the LaTeX kernel or in the class files (at the time “style files”). When European users started using LaTeX with different languages than English, the need for translating those fixed words emerged.
The first versions of babel patched several commands from the kernel or the class files. When LaTeX2e was released, for every fixed word a command was defined, so for babel it was easier hooking into LaTeX by changing the meaning of those commands. Thus, for Italian, it was easy to define \contentsname to mean “Indice” and not “Contents”.
The babel package stores the fixed tags for a language in the command \captions<language>. For Italian we have something like
\def\captionsitalian{%
\def\prefacename{Prefazione}%
\def\refname{Riferimenti bibliografici}%
\def\abstractname{Sommario}%
\def\bibname{Bibliografia}%
\def\chaptername{Capitolo}%
...
}
When babel switches from one language to another, it executes the corresponding \captions<language> command. The first switch happens when \begin{document} is being executed. Of course, if babel is not loaded, nothing happens and the default fixed tags for English are used.
Coming to your problem, you have two strategies:
\documentclass{amsart}
\renewcommand{\contentsname}{List of abstracts}
\begin{document}
without babel. If, however, one of your abstracts is, say, in French, you'd like to load French and English with babel. The redefinition above would not work, because of the execution of \captionsenglish at \begin{document}. Here's the correct workaround:
\documentclass{amsart}
\usepackage[T1]{fontenc} % French wants it
\usepackage[french,english]{babel} % English is the default
\addto\captionsenglish{\renewcommand{\contentsname}{List of abstracts}}
\begin{document}
In this way, the redefinition of \contentsname is appendend to the list of commands executed by \captionsenglish. So, any time you load babel, a change to a fixed tag must be made with \addto\captions<language>.
\documentclass{amsart}\def\contentsname{foo}\begin{document}bar\end{document}compiles without mishap, here. Same with\renewcommand. Can you post some minimal code? – jub0bs Jan 09 '14 at 15:10babel? I guess so. Please, make a minimal example. Also look for\addtoandbabel. – egreg Jan 09 '14 at 15:24babelsolve the problem. Thanks a lot. If you wish, answer. – Sigur Jan 09 '14 at 15:43