Inbound links are links that are directed towards your website from other domain. Also knows as backlinks. The number of inbound links is an indication of the popularity or importance of that website.
Outbound links are links that are meant to take you elsewhere. These are links that are going to direct you to another specific webpage or website altogether. There are two types of outbound links dofollow & nofollow.
The dofollow link is the normal link, passes on Google PageRank juice from your webpage to the targeted webpage.
A nofollow link is the abnormal link. It does not pass on any Google PageRank juice to the targeted webpage but instead, it blocks off the Google PageRank flow.