When you provision a new Azure Website, you can connect to it via HTTP or HTTP/S, if you choose to connect via HTTP/S from your own domain name you will receive an SSL warning as the Common Name for your website is not in the SSL certificate. This is because the default SSL certificate is a wildcard certificate for the azurewebsites.net domain.
You can of course bind your own globally trusted SSL certificate to an Azure Website, click on you Websites, and then on the website you want to bind a certificate to. Click on the Configure option and scroll down to Certificates. Click Upload a Certificate.
The Certfificate you tryv to upload must be in the PFX format that has the associated Private Key, if you have generated a CSR your computer and then requested the SSL certificate from GoDaddy for example the CSR will hold the Private Key required. If you need guidance on how to convert a GoDaddy (or any other vendor) certificate into a PFX file, you can review this post
When you upload the certificate you will need the corresponding password.
Scroll down to SSL Bindings, and from the drop down select your domain, please note the domain must match the Common Name configured on the certificate or the domain must be set as a Subject Alternative Name (SAN) within the certificate.
Custom SSL bindings are subject to a price increase. Click Yes.
From a new browser window you should be able to browse to the website and see that it's configured with your SSL certificate.