Is it the look, the design, the layout, the content, is it too design-led for the kind of customers it would be suitable for?
I think your site is too design-led at present, design as in looks/visuals, rather than design as in carefully thinking through a problem and designing an appropriate solution. Some websites can be looks-led, some funtion-led, some technology-led, some content-led, some SEO-led, which is fine but first and foremost they should be led by common sense, which means getting the balance right (don't focus too much on looks/form if it sacrifices function, e.g. being able to read the site).
With any ecommerce website you need to assess your market and see how you fit in. The baby products market is an extremely competitive one, just google for baby clothes and see how many different online shops you find. The more competitive and saturated a market, for small startup businesses the more you have to focus on a niche, and once you find your niche or niches, then capitalise on them.
If you think that organic, natural, eco friendly baby products is your niche then you really have to emphasise this in your website, especially if you want to attract people wanting this from the search engines in the first place, and keep them interested in your site once they arrive. I think that at present your main wording, category and product headings do not emphasise organic or eco/environmentally friendly, neither from a first glance view, nor from an SEO view (i.e. your site is not search engine optimised with an emphasis on organic, not in its home page, categories or products). If you think it is important to use organic cotton or have eco-friendly products emphasise why (upfront on your home page, in articles etc).
You might also have mixed messages on your website that are attracting visitors looking for products you do not supply. For instance organic generally is associated more with food than clothes, baby food is a popular search term, you have a Feeding category on your organic website, but you do not provide organic baby food. So make sure you are not attracting visitors looking for organic baby food, check your visitor stats to see why people are visiting your site.
Once you know why people are visiting your site, you also need to assume that they will look elsewhere too, so check your competitors in these areas.
Also put yourself in the place of visitors coming to your site for the first time, who have never heard of you before. Does your site give the visitor enough confidence in you to make a purchase? This is even more important in a very competitive market. There are ways you can improve on this. Make it easy for the visitors to find out who they are dealing with. Change 'Profile' to 'About Us'. Think about changing your anonymous PO box address to a real address and your anonymous 0845 number to a real geographic number. Provide your full company details.
Try to avoid using manufacturer's descriptions for products, especially when they are american descriptions using color instead of colour.
Looks-wise I would agree with the other posters that your text is difficult to read. You may think it is fine, if so check it on a number of different PCs and monitors (check it at your local internet cafe or library). Different monitors will have different brightness contrast settings so it may be the case that your settings are lower than on other PCs, and therefore the problem isn't so obvious on your particular PC. There are also some inconsistent navigation elements which might put some users off, for instance the add to cart links are not obvious, and the subcategory navigation is a little confusing.
On IE6 the basket is displayed under the menus on the left, not to the right of the menus.