<b> ... </b>tells the browser to render the contained text in a distinctive bold fashion. The HTML standard defines this as a physical style as distinct from <strong> ... </strong> which is a logical style.
Here's an example.
This is <b> style
The meaning is that the physical style directs the browser to display in a bold typeface whereas the logical style directs the browser to display with a stronger emphasis leaving it to the browser to decide how this is achieved (underlining or distinctive colour might be used).
All browsers honoured this tag in the same way.
See also <strong> and the general notes on text styles.