Everything worth knowing, nothing that isn't.
How it reaches you
When someone texts your number, the mobile-originated message is delivered to your application via a webhook in real time, so you can process it programmatically. See /answers/what-is-mo-vs-mt and /answers/what-is-a-messaging-webhook.
What number receives it
You need a number capable of receiving: a long code, toll-free number, or short code. A one-way alphanumeric sender ID cannot receive inbound messages. See /answers/what-is-long-code and /answers/what-is-short-code.
What it enables
Two-way support, reply-to-confirm reminders, surveys, keyword campaigns, and mandatory STOP handling. See /answers/what-is-two-way-messaging and /answers/how-to-handle-sms-opt-outs.