Glenn Berry explains the two purchase models available with Azure SQL Database, as well as the various service tiers within each model:
The older pricing option is the DTU-based SQL purchase model, where a fixed set of resources is assigned to the database from three performance tiers, which are Basic, Standard, and Premium.
For Standard and Premium, there are multiple service tiers, which are classified according to how many Database Transaction Units (DTUs) they provide (along with their included storage and maximum available storage). The Premium tier is designed for I/O intensive workloads, and is fault-tolerant.
The Database Transaction Unit (DTU) is based on a blended measure of CPU, memory, along with storage reads and writes. The DTU-based performance levels represent preconfigured bundles of compute, memory, and storage resources designed to drive different levels of application performance. If you do not want to worry about the underlying resources and prefer the simplicity of a preconfigured resource bundle while paying a fixed amount each month, you may find the DTU-based model more suitable for your needs and easier to understand.
Glenn does a good job clearing up some of the complications around pricing for Azure SQL Database.