It never occurred to me to write about this before because the difference between these two pages always seemed to be really obvious to me. The number of people I have seen asking about this on various forums clearly indicates that it is not as obvious to everyone though and so I have decided to cover this topic now.
One thing you may see mentioned quite a lot when it comes to getting your site set up so that search engines can find it is "Landing Pages". Many people think of their home page as the landing page for their site whereas for most sites the home page is one of the few pages that you would not necessarily consider to be a landing page. A landing page is the one your visitors first arrive at on your site and with the way that search engines work this will hopefully be the page that contains the information that they are actually looking for. For a site selling things a landing page will usually be a product page. For an information site (such as this one) a landing page will be an article. The home page does not usually deal with a specific product (except for single product sites) and is unlikely to be an article and so is unlikely to be the page on your site that contains the specific thing that people are looking for.
Instead the home page is the page that ties all the product or article pages together and basically provides a central point where those who have already found your site by landing on one of the product or article pages to find out what other products or articles that you have to offer from your site. The home page should identify the purpose of the site and give a clear indication of the scope of the site itself. If you visit the home page of this site you will find a list of all the categories that the articles on the site have been grouped into - it gives an idea of the range of topics that the articles cover and also groups the articles together with other related articles. It is extremely unlikely that anyone will be actually searching for the information on this site's home page because it is very general in nature and mainly serves to tie together all the categories into which the articles have been placed. The same is likely to be true of other site's home pages as the purpose of the home page is to cover what the site is about.
So if the home page covers what the site is all about then what is the purpose of the 'about' page? Well when someone finds an article or product on your site they can find out more about the other articles and products on your site by visiting your home page. What they can't find out that way is anything about you - the person or company that is responsible for providing the articles and products on the site. To find out about who it is that has provided the site they will want to visit your 'about' page. The about page tells them about you and what sort of authority that you have in providing the products or articles on your site. It tells them how long you have been in business for and more about the specifics of the business you are in. It is the information on the 'about' page that let's your visitors know that they can trust what they find on your site because they know who you are and by what authority that you are offering the information or products.
There will be a few instances where the about page will be the landing page that someone is searching for. Someone who has heard of you and searches for you on the web should find your about page as the number one result of their search (assuming that there are not a lot of other site's out there being created by people with the same name). As other sites are not so likely to actually publish information about you there shouldn't be much competition for this particular search.
So basically the home page is the page about the site while the about page is the page about the owner of the site. These are two completely different things serving completely different purposes with respect to the site and so any site will need to have both of these pages. This should be the case even with a small site since by keeping these two very different things separate you will improve the chances of your site being found in searches.
This article written by Stephen Chapman, Felgall Pty Ltd.