In this example I've used the Frontier theme, which is an excellent theme with full customizable facilities and can be adapted to different niches. Below is what you would see when you activate the theme and click on all pages on the dashboard:

And below is an example of the customized theme:

Basically I haven't changed the layout. I've changed the background color and removed the Frontier Logo and added a banner head instead (which I made using Gimp). I didn't like the border around the text and sidebar so I removed them. I reduced the size of the page title (Home) which I thought was far too large, changed the font-family and font-size and added a horizontal rule and h1 and h2 headers.

In the sidebar I added a different background color which helps to distinguish it from the main text. I changed the background color of the widget titles and also changed the font and font size and capitalized and letter spaced them, finally changing the font and font size of the widget text and the background color of the footer.

I also removed the link, Frontier Theme, on the right hand side of the footer, as if visitors to the site clicked on it, it would take them to the theme designers website, which I don't think visitors would really appreciate. If you wish you can put an accreditation in the footer by going to footer php in the stylesheet.

I hope this gives you some idea of what can be done by customizing a theme. The above example is purely for demonstration purposes, but there are many ways a theme can be customized to suit your niche or improve the sites appearance. The custom css I used to make the changes are on the next page, there are numerous ways it can be customized to suit a particular niche.