Previously, Azure used to provide its services via two portals, but recently, Microsoft discontinued the ASM (Classic) portal. However, if you have any services that were running in the classic portal you do not have to worry about them because they have been migrated to Azure ARM portal. Considering that these services would follow the old ASM model. Also, you will note that in the new Azure portal there are two flavors for them. For example, there will be Virtual Machines, and Virtual Machines (Classic).
Historically, Azure services were provided via one portal before 2014, the classic portal, which can be accessed via the following link https://manage.windowsazure.com/. As of now, this portal will redirect to the ARM portal.
The model that was used for that portal is called the ASM model, within which each resource existed independently. You could not manage your resources together, you had to build up and track each resource. For example, you will have to manage the networks from the NETWORKS blade, and the same goes for the storage, virtual machines, and so on. So, when your environment gets bigger, there will be chaos in the management scheme. You will have to know which Azure Virtual Machines are using which virtual networks to do its communications, and that might lead to some critical situations, such as reaching the limits of the allowed number of public IPs, and whenever you need to add a new public IP to be used for a VM in your environment, you would not be able to do so because of the poor management of resources. This would not be your only concern while working with the ASM model. If you want to delete a solution with multiple resources, you will have to do it with each resource manually, and so on.
This is how the classic portal looked: