site wide links are links on pages throughout the site ... they used to work great in early days but now they seem to have lost their value... They may send few visitors than one single link, but don't expect them to help you increase your PageRank. you might also want to read this Beware of Site Wide Text Link Ads
Sitewide- found on every page of your site. Beneficial or not- depends on you really. If your site is new, and a majority of your links are sitewides you might be flagged. The advantage of sitewides- the chances that a person will click on your link is higher when he sees it on every page. If you possibly had to choose between a sitewide on a site with 100 pages, and 100 homepage links on different sites, you'd obviously choose the latter.
I want to ask, if I have one box for my link partner but only in my home page, can it be considered as sitewide links?
one more question if i am doing site wide with a directory if it will be beneficial or not my site is not new one.