301 redirect is a special information(301 code) sent to browser or search bot by your server on certain page visit. 301 code means moved permanently.
To keep your site searchable by search engines like Google you need to apply 301 redirects to old pages after url change. Without this information search bots can't understand (in most of the cases) that page url was changed, but the content is the same and valuable for to be visible in search results. So, if your income depends on organic search, there is a very special reason to do 301 redirects in right way.
1. You decided to change url for some page to make it more relevant to page content for better user experience.
2. You deleted some page/pages and created new page with new but similar content.
3. You replaced whole site with newly built one and you have new url structure. You will need to do bulk 301 redirect. Generator may help with your list.
If You already have redirect code like Redirect 301 "/old" "http://example.com/new", note that these rules are handled with "mod_alias", but not "mod_rewrite". While both modules can do permanent redirects, "mod_rewrite" is more functional, what will do rewrite system more flexible and can help you in the future. For examle, "mod_alias" can't fully handle query strings. These Apache modules have separate flow and Redirect 301 rules can conflict with Your new "mod_rewrite" rules. If you have small amount of Redirect 301 rules, we can recomend to rewrite these rules with "mod_rewrite" functionality to keep the logic clean. For simple redirects and some enterprise solutions mod_alias can be a good choice too. Mod_alias documentation here. Mod_rewrite documentation here.
Maybe, most popular server for WordPress is Apache. Best practices for 301 redirects is to use htaccess file directives. Apache server users can locate htaccess file in the root directory. You can use FTP connection or special plugins to edit your htaccess file. While many SEO plugins provide a possibility to add and manage 301 redirects in WordPress admin panel, we can't suggest to use 301 redirect WordPress plugins because htaccess redirects are much faster and, therefore, better for user experience and for SEO in many cases.