The 'optional excerpt' box helps you to specify the part of your post which you want to show up when someone searches your site by categories.
The default option is simply to leave this block blank - WP.com will then show either:
- the first few lines of your post, or else
- that part of your post which comes above a <---more---> tag, if you use them to subdivide your posts.
Why would you use the 'optional excerpt' box ? Possibly because you wanted to highlight some 'killer text' from the within the middle of an article, rather than the opening sentences of preamble.
That might be required in some cases - but in general, it's best avoided. Journalists call this approach 'burying your lead'. The implication is that you should hit from your very first sentence, because people simply might not read any further.
Copyblogger and Pearsonified have some interesting ideas on this - both arguing that you should always strive to put the 'meat' of your articles as high up as you can - and indeed even within the headline if you can possibly manage it ...