Dematerialised securities are those that can be held without evidence of ownership in the form of certificates. Ownership is usually instead recorded in a depositary. Shareholders usually receive regular paper statements of their holdings (not dissimilar to bank statements).
The advantage of dematerialised holdings is that they are far cheaper to administer. The elimination of paperwork and the automation that makes it cheaper also makes it faster. Some modern systems can transfer both payment and ownership immediately. All dematerialised systems are faster and cheaper than dealing with paper certificates.