When starting a new project that will be hosted in Windows Azure, you have to select a VM Size. The sizes range from extra small to extra large. These sizes are a fixed package. For example, when a small VM is selected you get 1 core running at least 1.6 GHz with 1.75 GB of RAM and 225GB of local storage.

VM Sizes offered in Microsoft Azure. Graphic comes from the Windows Azure Cloud Services PowerPoint presentation found in the August 2012 Windows Azure Training Kit.
Note: When it comes to CPU Speed the 1.6 GHz is considered a minimum value. It is possible that the actual CPU will be greater than 1.6.
Why is the VM size important and is there any guidance around selecting a VM size for an application?
The rule of thumb is to select the smallest size that can run the application. The first reason for this is price. The smaller the VM the lower the price. The next reason for the rule is the number of instances can be changed with a configuration setting while the application is running. To change VM sizes the application will need to be re-deployed. The third reason for the rule is the more instances that are running the redundancy there is. This means that when an instance fails a small number of users are impacted by the failure. It also give the load balancer more places to send traffic in the case of failure. The last reason for the rule is more instances running allows for more work to be completed at one time.
As with all rules of thumb, there are times when the rules needs to be broken. There are situations where more cores is the correct answer. Examples of this include processing of Big Data, video processing and stateful services.