A concatenated SMS is a long message split into several parts, each carrying a small header so the handset reassembles them in order into one message; each part is billed as a segment.
Concatenation is how a message longer than one segment travels. Each part carries a user data header with a reference number, the total count and its position; the header takes 6 bytes, which is why parts hold 153 GSM-7 or 67 UCS-2 characters instead of 160 or 70. The receiving phone waits for all parts and shows one message.
Parts can arrive out of order or, rarely, one can be lost, in which case the phone shows an incomplete message. Very long texts are also more likely to be filtered as marketing. Six parts is a sensible ceiling.
At SMSMeteor: messages are limited to 6 parts per message; the composer shows the part count as you type, and the API rejects longer texts with text_too_long.