TLS assumes a reliable, ordered stream, which UDP does not provide. DTLS keeps the same handshake, certificates and ciphers but adds sequence numbers, a retransmission timer for handshake messages and tolerance for packets that arrive out of order or go missing. A cookie exchange protects servers from being used in amplification attacks.
It is the standard security layer for CoAP, written as coaps, and for LwM2M, where pre-shared keys are popular on very small devices because they avoid certificate parsing. Connection IDs, a later extension, let a session survive a change of IP address, which matters for cellular devices whose NAT mapping expires during sleep. The trade-off compared with TLS is less ubiquitous tooling and the need for the application to handle its own reliability on top. See CoAP explained.
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