A toxic link is anything that has a negative impact on your site's rankings.
The most common toxic link is one that sits on a site that has been completely de-indexed by Google. So not only does it offer no link-juice value, it has a negative affect.
The second most common is any links on sites that may be indexed, but don't rank for any keywords, get little or no human traffic, have no social signals. Typically these are sites that are neglected and commonly suffer from some degree of -50 or -100 penalty themselves. A lot of general free web directories fit in this category, as do most low-ball Pligg and Scuttle bookmarking sites. They're 'kraplinks' and Google knows it. If used aggressively and in bulk, they'll just drag your site down.
Another toxic link is one that's been manually flagged by a Google reviewer. You might have a link, say, in a guest post on an otherwise high authority site that gets subject to manual review. You may then have a broader penalty applied to your site ranging from a -50 penalty (you cant rank any higher than the 4th or 5th page of google, a -100 which traps your keywords near page 10, or result in your site being completely de-indexed.