A homepage intro can go a long ways, even if it's just a two sentence blurb. It doesn't need to be three paragraphs, or even one, explaining the entire history of the company, but a little something to ensure the user that this site is what it looks like will help.
Most likely the user will understand instantly that they're on an ecommerce site. Then the question becomes, what is this site specializing in? Is it the stuff I just searched on google? Or is their focus in something not well related, and they just happen to have a page with products similar to what I'm looking for.
I've personally found myself in the above situation, where I'm browsing around for something, and via organic search, I come across an ecommerce site with some similar things, but I have no idea what the site is specializing in because it doesn't have a clear theme. In these cases, I might see the stuff I'm looking for, but I'm still left a little uneased because I've never seen this site before, and it's not clear they exist to sell X related product, rather, they just happen to have a page with it amongst other products with no apparent theme.
Basically, if you're an ecommerce site, and you're not amazon, or the online shop of a major department store, you probably have a specific theme. Example: Hair care products, lawn care and power tools, etc. Make that clear. Users are much more at ease when they completely understand where they are, especially when they're about to pull out their credit card, and they're much more likely to stay on your site.