Two-way SMS lets recipients reply to your messages; it requires a numeric sender (a dedicated or shared number) because alphanumeric sender names cannot receive replies.
Most application traffic is one-way: the message goes out from a name or a shared number and there is nothing to reply to. Two-way messaging uses a real number as the sender so that replies come back, are matched to the conversation and are forwarded to you by webhook or shown in an inbox.
It is the basis of confirmations (reply C to confirm), keyword campaigns, support over text and, in the simplest case, STOP handling. The number is rented per country, because replies must terminate on a number the local operators can reach.
At SMSMeteor: replies are an option on a campaign: a two-way number per destination, replies collected in the panel or answered automatically by keyword rules, and forwarded to your webhook.