Serverless hosting is when your website runs off a cloud infrastructure. You do not need to buy a physical server and maintain that server which can be very beneficial financially. Usually the serverless provider will charge based off of the storage used so a smaller website will only have to pay when actively is happening on their site and not 24/7. One site I found a lot of my information at and learned more about serverless hosting was at berkaweb.com
One of the most popular reasons to use serverless is it costs less and it can be a better option for smaller businesses. Another popular reason to use serverless is its security. Since it is a cloud based platform you can add additional security like firewalls and malware protection.
IBM Cloud is one of the first serverless providers I found. IBM has a free version that has requirements that your website must not go over to qualify for the free version, and those are CPU usage, Memory, and incoming requests.
ibm.comAWS Lambda is a created by Amazon allows you to create serverless websites. Lambda runs your code on their provider and you need to create a function on their website which then allows you to upload your files. You then need to setup a Amazon API Gateway and complete some steps with the API and functions and eventually get it up and working. The process of Lambda seems a little complicated, but there are many steps provided on the website and others to get you through it.
aws.amazon.comThere are many serverless providers out there and it seems that the a smaller website or company can benefit from using serverless. with is security and cost I think it is a good option, though it seems with some providers it may be a little complicated to get setup initially. Once everything is up and going it can be great.