The b element represents a span of text to be stylistically offset from the normal prose without conveying any extra importance.
It was originally used to tell the browser to make the enclosed text bold. While the b element is widely supported in browsers, its use is not recommended for this purpose since CSS can be used to achieve the same effect on a more semantically-appropriate element. In HTML5, b has been re-purposed to signify text this is offset in some way, but is of no greater significance than the surrounding text.
The b element should be used as a last resort when no other element is more appropriate, as it has no semantic value other than indicating that the contained text should be stylistically offset in some way (i.e. it’s like a shorter span element). For visually similar elements that do provide semantic meaning, consider strong, dfn, h1-h6, or abbr.
In the following example, objects in a text adventure are highlighted as being special by use of the b element.
<p>You enter a small room. Your <b>sword</b> glows brighter. A <b>rat</b> scurries past the corner wall.</p>
In this example, the b element is used to indicate both a company and a product name. Disambiguation via CSS is accomplished using the class attribute.
<p><b class="org">Acme <abbr title="Corporation">Corp</abbr></b> is pleased to introduce the <b class="product">Widget Blast 3000</b>. This is a miracle of modern science that will simplify your life, fry an egg, and even put your kids to bed.</p>
The b element makes a lot of sense for use as a wrapper for proper names (e.g. people, companies, products, locations) as they may be offset from the surrounding text in some way, but are not semantically meaningful.
Internationalization topics related to the b element:
As the b element has no inherent meaning, you should not use it to convey meaning; there is probably a more appropriate element for that. Headings should use the h1 to h6 elements, stress emphasis should use the em element, importance should be denoted with the strong element, and contextually-important/highlighted text should use the mark element.