How a company can improve the quality of products or services, so that they are of even more value to existing and prospective clients?

You've asked a general question, so the answer will be generalized too:

Improving the quality means Improving the product/services quality dimensions values which are: (aesthetics, features, conformance to standards, performance, durability, reliability, servicability and the preceived quality of the product/service)so you have to start measuring -using 'statistical models'- the current values of those dimensions, to state whether enough or not, then you start designing for improvement if you aim to improve.. and after the implementation of your solution/design, you control the improvement statistically to measure performance and other aspects improvements..

Only results of your measurs which can assure either the quality is improved or not.

simply by R&D in accordance to the feedbacks

AGREED WITH KRISHNA & MY BRO, ARINJAY,,,

Agreeing to the input given by Mr. Mohammed Ismail, if I may make some addition.

Seller has to fulfill the claims made for the product / services and if any variation persisits then scope of improvement exists.

Feedback from users / customers would create another opportunity for improvements.

If products: let your dedicated R&D do the job in terms of quality assurance improvements (processes) and quality control improvements (finished products) in terms of aesthetics, features, conformance to standards, performance, durability etc.)

If services: service sector companies usually do not have a dedicated R&D department but can nonetheless improve service as their main offering through a combination or Quality Assurance and Quality Control.

Service improvement as in customer service is not the intent of the question, I think as it is related to an important but non-core function of business. 

The quality of the products need be improved based on and to strengthen "average utility period" of the similar products available in the market compared to your price level.  If your product is improved to have better average utility period for the price paid you will have an edge for the product in the market so as retain and attract your existing and prospective customers. 

First of Quality of the Product and allied Service are two different things.Existing Product can be improved by installing Automation in Operational system so that required accuracy of the product can be maintained.Enhanced equipments in Laboratory are also improve the quality standard before delivering to the Customer.It act as secondary and final checking before final execution.New product can be designed with a new composition as adviced by the OEMs.

Service can be improved  by tacking intransit movement,attending phone calls,24*7 hasslesless transparent fair communication.The main part of Service is timely delivery of the product and ensure availability of Product at customer premises so that downtime is zero.Implementation of Stock record system and consumption record system at Customer premises helps a lot in the service improvement.

On time delivery of goods and quality of goods need to meet customer requirements

Very simply by measuring customer importance and company performance , try to improve your performance according to these importance

Good Day!!!

Agreed to the answer given by Mr. Khatim.......