If your website gets a lot of traffic from search engines, and Google in particular, then you need to care about all the things that Google wants you to care about, including 'First input delay'.
If you don't pay attention to this metric then you may find Google lowering your site in their rankings and thus you get less and less traffic to your site. Usually, we aim for more traffic, not less :)
First input delay
There are many great articles explaining what First Input Delay is, so go read them if you need to, and then come...