This is something that is quite common in large white collar UK companies who are trying to downsize, or perhaps after a takeover.
Unlike Conventional redundancy (being laid off), voluntary redundancy is just that - voluntary. Your company makes you an offer to leave, which you can choose not to accept. Because the offer is voluntary, the cash you are given is often significantly higher than the basic statutory requirements to entice you to accept the offer. It may also include things like payment in lieu of notice.
Legally, however, you are resigning, and the fact you're receiving a large amount of cash is incidental. This means that you are not entitled to unemployment benefit and the various other things that most unemployed people are. On the other hand, the amount of money you're offered should more than compensate for this.
Voluntary Redundancy may be targetted (ie your manager offers you a package directly), or it may be offered en masse - "those who may be interested in a redundancy package, speak to their manager".
Is it a good thing to turn down a voluntary redundancy offer? In most cases, probably not. Once you've been offered this, it means that you'll probably be offered redundancy again. But next time it may be compulsory, with a significantly smaller package to go with it. My last employer had an over 90% acceptance rate with their voluntary redundancy packages, probably related to their size.