I'm glad to say that's quite easy with CDF, but the cell will only be available to users with the CDF Player installed.

Select the output cell in Mathematica, and go to File > CDF Export > Web Embeddable. Make sure Current selection is selected in Step 2. Choose a location to save the file, preferably somewhere in the directory of your site. The rest should be pretty easy to follow.

If you need the file to be accessible to users without CDF Player installed, you do indeed have to use webMathematica. It looks like the brain-segmentation example uses a combination of webMathematica and a Flash applet.

Demonstrations on the Wolfram Demonstrations Project are displayed as CDF files. CDF files are essentially Mathematica notebooks without input functionality, and on the Demonstrations project they're just single Manipulate output cells. If you want to make a CDF, you just need Mathematica.

The webMathematica demos are very dated, likely created well before CDF was even in development. All three interactive demos can be easily recreated with Manipulate and CDF. If you want to make a webpage, you can try embedding a CDF in HTML, or using the Wolfram Programming Cloud.

It should be noted that webMathematica is essentially a legacy product, as Wolfram has refocused its web efforts on new technology like the Programming Cloud.

WebMathematica and CDF are separate things. You said:

If you go to the webMathematica webpage and look at the examples, the code can only be downloaded in Wolfram language.

What webpage are you refering to? Can you link me to specific example? It sounds like you are talking about a CDF example - not a webMathematica example.

Before making your own webpage, please make sure you can get basic examples like the following to work: http://reference.wolfram.com/webMathematica/tutorial/BasicExamples.html#9976049

If you have trouble getting the basic webMathematica examples to work in webMathematica, I would consider contacting Wolfram Technical Support.

I'm sorry. I'm not sure I understand. Which file are you talking about? When you say Webapp, do you just mean a webpage made with webMathematica?