301 redirect is a HTTP status code that means a piece of content has permanently moved from one URL to the other.
If your company website was http://www.example.com and you changed your domain to http://www.yournewwebsite.com, you would place a 301 redirect on each page of the first website and point it to the same page on the new domain.
Using a 301 redirect means that anyone who inputs that URL is automatically redirected to the new page. You should monitor how much traffic comes to your new site as a result of the 301 redirects and ensure you maintain ownership of your old website until traffic from this source is minimal. Consider including a message on your new website so redirected browsers take note of your new domain.
A 301 redirect also influences search engine spiders, meaning they will start to show your new domain in search results.