Everything worth knowing, nothing that isn't.
Anatomy of an E.164 number
A '+' prefix, then a 1-3 digit country code, then the national subscriber number — 15 digits maximum in total, with no spaces, dashes, or national trunk prefixes. The '+' tells every network the digits that follow are internationally routable, removing the ambiguity of local dialling conventions. See /answers/what-is-msisdn.
Why E.164 prevents delivery bugs
The commonest cause of failed A2P sends is a number in a local format — a leading 00, or a national 0 that should have been stripped. Normalising every number to E.164 before submission, and validating it with HLR Lookup (which also reveals the current, possibly ported, operator), removes an entire class of delivery failures. See /products/hlr-lookup.