classic..
inbound link: simply any link that is pointing to your web site/page
outbound link: simply any web sites/pages you are linking too
backlinks: simply all the links that are pointing to your website/page
Inbound: The purpose of gaining inbound links is traffic by way of the SE's..the more,the higher quality of website that link to you is that your site will eventually rank higher in the se.
outbound: You are essentially giving a website a vote (you feel the website has useful content) ..the search engiines are basically tallying the votes ! and ranking you compared to your competitors.. problem is these "votes" can be purchased ! lol ..or advertising.
People can sell a link ...link advertising .. so the search engines add to their algorithims formulas to try and sort out in the linbound links are natural or purchased..most likely giving a natural link more weight. ( a natural link is one that a was given simply because the person thought the website had useful information/product/content..)
checking your backlinks can be important.. you want to see if people are really linking to you (especially if you purchase an adevertisng link or are reciprocating links , you want to check for broken links , etc..