<big> ... </big>tells the browser to render the contents in a bigger than normal typeface.
Here's an example
This is <big> style
The effect is probably easier to see with big text included in normal "running" text. It is generally equivalent to <font> with the size attribute set to +1. Here is text with font size set to +1 and here is big text.
MOS3 does not honour the tag. All other browsers handled it correctly.
See also <small> and general notes on text styles.