IaaS, PaaS, and SaaS are the three classic cloud service models, each ceding more to the provider. IaaS (Infrastructure) rents raw compute, storage, and networking (EC2) — you manage the OS up. PaaS (Platform) gives a managed runtime to deploy code onto (Heroku, App Engine) — you manage just the app. SaaS (Software) is finished software you just use (Gmail, Salesforce).
Worked example: to run a web app — IaaS means you provision VMs and install everything; PaaS means you git-push code and the platform runs it; SaaS means you skip building it and subscribe to an existing product. FaaS/serverless sits between PaaS and SaaS. Gotcha: moving up the stack trades control for convenience and can trade cost and lock-in — PaaS and SaaS speed you up but constrain customization and can be pricier or stickier at scale — so the right layer depends on how much of the stack is your actual differentiator versus undifferentiated heavy lifting.