I know some homeschoolers poo-poo the notion of doing "honors" courses in high school or just don't care, however, I'm on the side of the fence that does care.
First, some colleges do in fact give extra weight for honors high school courses when considering an application for admission. Take a look at the application/admission requirements page of any college's website and it will state such if they do. Some of the colleges my high schooler is considering do give the extra weight toward a high school GPA, so that is one reason I have him doing honors level work in some courses. Second, I feel it can only benefit the student, especially if he/she is considering a college major related to that subject.
My high schooler is intending to major in a biological sciences field, so it only makes sense to me to have him complete an honors course in biology this year (ninth grade).
But what makes a course an "honors" course? Here is where you will find a variety of opinions, and you know what? ... that's okay.
We are using Apologia Biology (2nd edition) along with the companion multimedia cd as my son's biology curriculum. On its own, could it be considered an honors course? That's left to your own interpretation. In my opinion, no. However, I personally don't feel there is any one right way to add to the text to bring it up a notch. One opinion on the matter was discussed at a high school homeschool seminar I attended over a year ago. The author of a book about homeschooling high school stated during that seminar the only way to make Apologia Biology an honors course was to do a complete science fair project in addition to completing the text in full. Now while I agree every bit of the text should be covered (and that means doing all the experiments and dissections), I do not agree a science fair project added into the mix is the only means of making the course worthy of an honors designation. That's the beauty of homeschooling. We're all entitled to our opinions and interpretations! Do what you feel is right in your heart. You know your child and his/her interests, passions, and goals better than anyone.
So, what am I doing to make the course worthy of an honors designation? Several things.
In addition to the companion multimedia cd, YouTube is a fantastic resource for additional videos to use with each module. I personally have a Pinterest board dedicated solely to biology videos to help me keep track of what I intend to use with each module over the course of our homeschool year. (As of the date of this posting, I have not finished lesson planning so the board is not complete.) Extra reading (online biographies, articles, books - both fiction and nonfiction, etc.), extra experiments, additional projects, watching related films and documentaries, viewing additional dissections available online (photos like those at Biology Corner or videos), and so on certainly count as they help to enrich the text. I have a couple of Pinterest boards set up for those types of things here and here. (The latter is a hodge-podge of things and contains a lot of general ideas for expanding the curriculum.)
I am also having my son complete many (many!) of the plates/pages from The Zoology Coloring Book and The Botany Coloring Book.
Both are excellent and provide additional details and information beyond the Apologia text.
Just my 2¢ on the matter.