Google for YouTube users providing play your YouTube videos on your site such as message board with embedded video player. can also customize the embedded code as your size suitable with your website.
First right click on your YouTube video select the Copy embed code option.
Step 2 :
Login to into your WordPress account go to the post option, change into your text editor mode Visual to Text mode then paste the embed code on the page. after that publish your post on your WordPress site. then you can see the embed video on your site.