SEO is also about making your search engine result relevant to the user's search query so more people click the result when it is shown in search. In this process, snippets of text and meta data are optimized to ensure your snippet of information is appealing in the context of the search query to obtain a high CTR (click through rate) from search results.
Another example when the “nofollow" attribute can come handy are widget links. If you are using a third party's widget to enrich the experience of your site and engage users, check if it contains any links that you did not intend to place on your site along with the widget. Some widgets may add links to your site which are not your editorial choice and contain anchor text that you as a webmaster may not control. If removing such unwanted links from the widget is not possible, you can always disable them with “nofollow" attribute. If you create a widget for functionality or content that you provide, make sure to include the nofollow on links in the default code snippet.
Google ranks websites (relevancy aside for a moment) by the number and quality of incoming links to a site from other websites (amongst hundreds of other metrics). Generally speaking, a link from a page to another page is viewed in Google “eyes” as a vote for that page the link points to. The more votes a page gets, the more trusted a page can become, and the higher Google will rank it – in theory. Rankings are HUGELY affected by how much Google ultimately trusts the DOMAIN the page is on. BACKLINKS (links from other websites – trump every other signal.)
Ever heard of Maslow's hierarchy of needs? It's a theory of psychology that prioritizes the most fundamental human needs (like air, water, and physical safety) over more advanced needs (like esteem and social belonging). The theory is that you can't achieve the needs at the top without ensuring the more fundamental needs are met first. Love doesn't matter if you don't have food.