What is a Link Profile?
A sites link profile simply put is the overall summation of links that points to a given site. If you break it up into 4 parts it will start to make sense. Relevant Links, Authoritative Links, Link Volume, and the Timing / Age of the links.
Relevant Links
These come from sites that are similar in topic to yours. The weight of the link doesn’t matter as much, why, because its an on theme link. These are important because they help convey to the search engines what the overall theme of the site is, IE. What keywords should they rank for.
Authoritative Links
Authoritative backlinks are ones that come from old, trusted sites, that have large amounts of links. A link from these sites pass lots of juice, and show the search engines that the site being linked to is one of quality.
Link Volume
The sheer amount of links pointing to a site is known as the volume of links to a site. This is a highly debated subject in the SEO world. Many beginners get caught up in this facet too much, thinking, many links is > a few links. When the fact of the matter is some sites with a few on topic, relevant, authoritative links can rank higher then a site with thousands of backlinks from unrelated sites. Although this is the case, having lots of links certainly wont hurt your site (in most cases, as long as the links are on topic).
Link Age/ Timing
The older the backlink, the better. Obtaining links for short periods of time in my opinion are a waste. A true, natural link will persevere, and generally stays on a site for a long time. The longer it stays, the more juice it will pass. This is built into the algorithms. Along with the age of a backlink, timing is also involved. Some topics become stale, with no new links for extended amounts of time. If a site begins to obtain lots of related, on theme backlinks, then that can be a sign to the search engines to rank that site higher.
Overall Link Profile
As you can see the overall link profile of a site can say a lot of different things. It is important to have a diversified link pattern. Sites that choose to take part in 1 of the 4 things are more likely to plummet when certain algorithmic updates occur. Keep your site safe by simply diversifying.