Most web browsers provide a Javascript API for invoking web services named XMLHttpRequest. You can use it along with other Javascript features to invoke Enterprise Server for .NET CICS REST web services from scripts on web pages and dynamically update the page content based on the response. Using this approach in web pages is often known as AJAX (Asynchronous Javascript and XML).
There are numerous online and print tutorials and references for XMLHttpRequest and AJAX.
Some additional configuration is required for CICS REST web services that will be invoked from a web page. See Configuring REST Web Services for AJAX.