When trying to obtain links back to your site from elsewhere on the web relevance isn't the most important consideration, it is the only consideration. The difference in the value of a relevant link compared to one that is not relevant is so great that it is not worth spending any time at all on trying to get links unless they are relevant.
The goal of having links to your site from elsewhere on the web is to receive targetted traffic. argetted traffic are real people who have an actual interest in seeing what your site contains. These are the people who will actually interact with your site rather than just moving on straight away looking for a more interesting page on some other topic.
If a link isn't relevant then you will have a much smaller percentage of the people on that page who actually follow the link to your page and a larger percentage of those who will move on straight away. If people are 100 times more likely to click on a relevant link than an irrelevant one (and the real difference is likely to be much much higher) and five times as likely to leave straight away (and again the real difference will be higher) then a page needs to receive 500 times as many visitors as a page where you have a relevant link in order to provide you with the same number of interested visitors.Even then you have the situation where those visitors have suddenly switched the topic they are looking at on the web and so will still be much less likely to follow through with whatever it is you want them to do on your site.
If you work backwards from the end result then for every minute you spend obtaining relevant links to your site you will probably need to spend several days working on irrelevant links to obtain the same result. So imagine how much more you can achieve if you spend those several days working on getting relevant links.
Irrelevant links are just as valueless to the search engines as they are to real visitors. While the extra links may get you a higher Page Rank or equivalent that factor is just about the least important of the hundreds of tests that the search engines perform to work out where to place your pages in their results. The two most important factors are how focused your page is on the specific topic and how many relevant links there are to the page.
Even relevant links that are marked as "nofollow" so as to instruct the search engines to ignore them are far more valuable than irrelevant links that are not so marked. Real people will follow a relevant link regardless of whether the search engines do or not and it is the real people you are trying to get to visit. Getting the search engines to visit and list your page isn't the end goal, it is just a way of obtaining more relevant links back to your site for th real people to follow.
Once you get real people to visit your site through relevant links you will have a percentage of those people who have their own site on a related topic and a percentage of those will see the relationship between their site and yours and will create a link to your site from theirs. These relevant links are the most valuable ones since you don't have to spend any of your time in order to get them.
Certainly you will get some interested visitors if you get millions of irrelevant links to your site or a few irrelevant links from extremely popular pages but you will get jst as many if not more interested visitors from a few relevant links . Those few relevant links will also be much easier to get.
This article written by Stephen Chapman, Felgall Pty Ltd.