I am finding it difficult to find a plain non/semi technical description online of what these are used for.
I come from a programming background but don't have a lot of administration experience.
Could someone give me a good basic description or resource of what the purpose and role of service applications and service accounts is?
Service application is something like a SharePoint plugin. Basically it provides some big piece of functionality you can later use througout your farm.
You can develop your own custom service applications, and also SharePoint includes a whole bunch of OOTB service applications, like User Profile Service, Secure Store Service, etc. Service applications are managed from Central Administration site.
Service account is an account under which a service application is running.
Service accounts also can be configured at Central Administration site.
Huge documentation hub regarding administration of service applications in SharePoint can be found on Technet:
