Definition
Concatenated SMS is a long message sent as several linked segments. A User Data Header (UDH) in each segment carries a reference number, the total parts and the part number so the phone can reassemble them.
The concatenation information element is defined in 3GPP TS 23.040. With an 8-bit reference number the UDH is 6 octets; with a 16-bit reference it is 7 octets. That overhead is why segments hold 153 (or 152) GSM-7 characters instead of 160.
In SMPP v3.4, a sender can build the UDH itself and set the UDHI bit (0x40) in esm_class, or let the SMSC segment the message using the sar_ TLVs or a single message_payload of more than 254 octets, depending on what the provider supports.
The handset shows the segments as one message once all parts arrive. If a part is lost or the reference numbers clash, the user may see fragments or nothing.
Each segment generally produces its own delivery receipt and is billed separately. Delivery reports should therefore be aggregated per message, not just per segment.
Example
UDH: 05 00 03 A7 03 01 = header length 5, IE 00 (concatenation, 8-bit reference), IE length 3, reference 0xA7, 3 parts in total, this is part 1.