The most critical reason welcome emails are powerful is because they set a precedence in the user’s email client inbox for future email delivery. If your subscriber sees the email immediately following their subscription they are very likely to open it. If it contains important information (like user account info) they are also likely to keep and not delete the email. This tells their email client (such as Gmail etc) that emails from you are important and should not be sent to the Junk filter in the future.
This is also why its important to tell users that you have just sent them a welcome or confirmation email. When someone fills out the form on your website, tell them to go straight to their inbox and open the confirmation/welcome email you sent them. Potentially include instructions in the email to ask the user to white-label your email address or add you to their white list to ensure future delivery.
Be sure to setup your welcome / thank you / confirmation email to help increase future delivery and customer satisfaction.