An A record helps your web browser find your website! It does this by using an IP address that points to your hosting provide(the company that holds on to your website files). The A record is one of the most important records in your ZONE file! It has lots of other uses to, but for most peoples needs that is all it does.
Side note: Search engines like Google, Bing, Yahoo, etc prefer that you have your site pointed by an A record vs. a forward or CNAME!