If you are not using blog services like blogger.com for your website and installed it in your hosting you need to check and maintenance (what is it?) it if you not doing it it can be a big problem (mostly security and spam comment)
Most people use WordPress in their content management system in their site if you using it you need to check for latest CMS update and don’t forget plug in and your theme need updated too
If you have famous blog you will have many spam comment from spammers even if you using akismet you may want to delete it manually if you log in in your blog
check your bandwidth and storage usage too if you have avalance traffic and if you use shared hosting most likely your website will be down because you exceed bandwith your hosting you better move to virtual private server
Ask your web designer are they offer maintenance for your website ?
They are now what things to do to make your website search engine friendly because search engine change constantly and your website need to keep up to date and there are a chance that your website get hacked and ask your web designer (here is the one of it )too if they do content updating ? that is if you can’t update your blog yourself of course