In terms of your website, this could be a visitor who has demonstrated interest in your website's content. This could be the visitor has filled out a web form, have downloaded content, have signed up for a newsletter or filled up the shopping cart and then left the site. Each type of interaction is assigned a lead score, a metric that is intended to help sales and marketing personnel determine where the visitor is in the buying cycle. If the potential customer is early in the buying cycle, it is usually the marketing department's job to nurture the lead.
Product qualified leads are contacts who've used your product and taken actions that indicate interest in becoming a paying customer. PQLs typically exist for companies who offer a product trial or a free or limited version of their product (like HubSpot!) with options to upgrade, which is where your sales team comes in. An example of a PQL is a customer who uses your free version but engages or asks about features that are only available upon payment.