Intel has historically achieved extremely high profit margins on its server chips. Intel charged thousands of dollars for each chip.
By introducing Arm server processors from multiple suppliers, it introduces competition into the server market which lowers the price of server chips, crushing Intel's margins, and improving price/performance.
Arm's 64-bit architecture was a clean sheet design announced in 2011 and based on RISC principles. There are technical arguments that it should be possible to implement this architecture with better power per MIPS or better power per FLOP. Power consumption is very important in huge cloud datacenters, because in addition to having to pay for electricity for the servers, there is an additional cost of cooling the data center with air-conditioning or pumping cold water through the data center. This means that power efficiency of server chips makes a big difference to overall cost of running the data center.
These technical advantages might help somewhat with cost. I think the bigger story is the crushing of Intel's historically huge profit margins via competition.
Note that Amazon's AWS cloud provider introduced servers using the Arm architecture a few years ago. AWS uses the brand Graviton for these servers, and they are already at their third generation called Graviton 3. These server chips are designed by AWS themselves under license from Arm, and manufactured at a foundry (probably TSMC). This allows AWS to specify exactly what they want on the server chip to fit in their cloud data centers.
In addition to AWS and Azure, other cloud providers have announced Arm servers, including Oracle Cloud, Alibaba, Cloudflare.
This is a historic turning point, with in server architecture shifting shifting to Arm.
Arm uses the brand Neoverse for their server chip designs.
See: https://www.arm.com/solutions/infrastructure/cloud-computing