What it means
In email, a bounce is a message that could not be delivered. A hard bounce means the address does not exist. A soft bounce means a temporary problem such as a full mailbox. In web analytics, a bounce has historically meant a visit where somebody looked at one page and left without doing anything else.
Why it matters to a small business
The two get confused in meetings constantly, and they call for opposite responses. A rising email bounce rate is urgent: it means your list is decaying and your sender reputation is at risk, which eventually stops your good messages arriving too. A high website bounce rate on a page that answered the question in one screen may be perfectly healthy.
The bit people get wrong
Hard bounces must be removed from your list immediately and permanently. Mailing a dead address repeatedly is one of the clearest signals to a mailbox provider that you are not paying attention, and the cost is landing in spam for the customers who are still there.