There are two answers because we have two different ways to receive incoming messages: On the web app or on the mobile app.
The web app shows received messages a little slower than the mobile version will. On average we will scan our services once a minute to check for any new messages that came to your number and they will be pulled into your account. Because the web version uses a 'pulling' method it may take around a minute to see your new incoming message.
The mobile app receives messages almost as quickly as they are sent. This is because the mobile app receives messages by having them 'pushed' to the app. The app doesn't scan a server once a minute for new messages, it receives them as soon as they are pushed.
*Note: There are many variables to how quickly a contact with receive your message and how quickly you will receive their response. Factors include, but aren't limited too: carrier sending, network settings, data settings, etc.