Why when i type in my domain name into search engine it says expired web domain?

First of all, which search engine are you talking about? Google??

Why would you search for your domain name anyway? Why not just type it directly in the Address Bar of your web browser?

If indeed you already tried typing it in the address bar but the page doesn't show, and tried googling it, and after clicking on the link (with your domain name), it says something like "Your domain has expired", then it probably is. Domain names are paid on a regular basis, depending on where you registered it, it can be between 1 year to 10 years.