Appendices that renumber cleanly
appendix, A/B chapters, counters that stay consistent.
Appendices that renumber cleanly
An appendix holds material that supports the main text but would interrupt it: long proofs, survey instruments, extra tables, implementation details. Readers expect appendices to be lettered A, B, C rather than continuing the chapter numbers, and expect the material inside to follow suit, so a figure in Appendix A is Figure A.1, not Figure 47. In LaTeX this is a single switch, not a restructuring job.
The switch
\appendix\chapter{Extra proofs} % becomes Appendix A\section{Lemma details}\appendix is a declaration, not an environment: there is nothing to close. From the point where it appears, the sectioning counters reset and switch to letters. In the report and book classes, every \chapter after it becomes Appendix A, Appendix B, and so on, and a \section inside becomes A.1. You still write only your own heading text; the “Appendix A” label and the lettering come from the class, exactly as chapter numbers did before the switch.
In article, which has no chapters, \appendix relabels \section instead: the first section after it becomes Appendix A. Everything downstream stays consistent automatically. The table of contents lists the lettered headings, and a \label placed in an appendix resolves through \ref to “A” or “A.2” without any special handling.
What renumbers and what does not
In report and book, figures, tables, and equations are numbered within chapters, so they pick up the letter for free: the first figure of Appendix B is Figure B.1. In article those counters run continuously through the whole document and \appendix does not touch them, so equation numbering simply carries on. That is normal for a short paper; only fight it if a venue explicitly asks for A-prefixed numbers.
When you want more
The appendix package adds refinements the plain switch lacks. Its appendices environment can print the word “Appendix” in each heading and in the table of contents (\usepackage[toc,titletoc,title]{appendix}), and it can insert a separator page announcing the appendices. For a thesis whose template does not already handle this, those options save manual fiddling.
One common mistake is writing the label into the heading yourself, as in \chapter{Appendix A: Extra proofs}. The class adds its own label, so the output reads “Appendix A Appendix A: Extra proofs”. Give the heading only the title and let the numbering machinery do its one job. If you have a single appendix, the lone “Appendix A” is a style question; most venues accept it, and some prefer an unlettered \chapter*{Appendix}.