First of all, make sure that you have correctly entered all SMTP details. Pay attention to trim all spaces before and after the texts you copy and paste into WebinarIgnition.

If that did not solve the issue, you probably have a shared hosting package. The problem with this type of hosting is that, in order to prevent people from sending spam from their servers, hosting companies block the communication over common SMTP ports (such as 25, 465, 587, etc). To fix this, you have to contact your hosting company and ask them to unblock the SMTP port needed by your SMTP relay, or provide you with an alternative port (sometimes instead of port 587, you'll be given port 2587).