Thinking about Doing Honors?

What is Honors, first of all?

Usually, by “honors”, Stanford means departmental honors. For most majors (but not quite all), honors means an honors thesis: a substantial project where you identify your own research topic, carry out the research, and write up your results. Just about every major offers an honors track, and in addition, several programs allow students from any major to participate in an interdisciplinary honors program.
Stanford does not use Latin honors (summa cum laude, magna cum laude, cum laude), but does award Distinction (based on GPA) to graduating seniors.
In addition, Stanford has a chapter of Phi Beta Kappa, a nationwide honor society that recognizes students for the excellence and breadth of their undergraduate scholarly accomplishments.

Next Steps

You can start discussing the idea of a thesis with people as early as your first year at Stanford, and as you move through classes up through your junior year, think about what types of questions you might be interested in answering with a thesis. It is most common that students apply for an honors program in winter of junior year, although some programs may have students enter as sophomores, and others allow you to join at the beginning of your senior year.
Your faculty are the best people to consult when thinking about honors, as having a mentor who can guide you in the project is essential. 
Your Academic Advisor is also always happy to discuss with you your thoughts and considerations about pursuing honors, and Academic Advising has written some general suggestions in Planning for Departmental Honors, which offers advice on finding a topic and a faculty advisor. We also have some thoughts on the pros and cons of doing a thesis.