Start from 2014 April, Microsoft Azure introduces a new instance tier of Virtual Machine – Basic tier. These instances are well-suited for production applications that do not require the Azure load-balancer (bring-your-own LB or single instance) , development workloads, test servers and memory-focused batch processing applications. 
There are few documents on what is the difference between basic tier VM and standard tier VM so here is a summary note based on my research
Azure price page makes it clear: General purpose compute: Basic tier – An economical option for development workloads, test servers, and other applications that don’t require load balancing, auto-scaling, or memory-intensive virtual machines.
Below are some detail context:
- Availability: Basic tier VM is only available on A0-A4 instances, standard tier VM is available on all size instances
- Disk IOPS: Data disk IOPS for basic tier VM is 300, lower than standard tier VM which has 500 IOPS data disk.
- Price: Single tier VM can have up to 27% less in price than standard tier VM.
- Feature cut: Basic tier VM does not include load balancing or auto-scaling. For basic tier VMs, you can add those to availability set for high availability, and implement your own load-balance mechanisms.
- CPU: Standard tier have better CPU performance than basic tier