Simple – covers the vast majority of any products you may sell. Simple products are shipped and have no options. For example, a book.
Grouped (bundled) – a collection of related products that can be purchased individually and only consist of simple products. For example, a set of six drinking glasses.
Virtual – one that doesn’t require shipping. For example, a service. Enabling this, disables all shipping related fields such as shipping dimensions. A virtual product will also not trigger the shipping calculator in cart and checkout.
Downloadable – activates additional fields where you can provide a downloadable file. After a successful purchase, customers are given a downloadable file as a link in the order notification email. This is suitable, for example, for a digital album, PDF magazine, or photo.
External or Affiliate – one that you list and describe on your website but is sold elsewhere.
Variable – a product with variations, each of which may have a different SKU, price, stock option, etc. For example, a t-shirt available in different colors and/or sizes.
Other types are often added by extensions or customization.

Examples of attributes include size, color, style, etc. Attributes are typically something that your customer would have more than more option to choose from and would select their preference via a dropdown. In the example below, "Color" and "Size" are the attributes.