A manual action penalty is when you get a notice from Google that someone from their staff has reviewed your website and found that it violated one of their webmaster guidelines. There are many different types but the most common is having to do with natural links that were built to your website.
An algorithmic penalty is when google updates their algorithm and your site may lose massive rankings but you were never notified by Google. Many people might lost 50% or more of their rankings in Google. That is a sign of algorithmic penalty. If you are ever confused or have questions regarding the type of penalty you might have please visit the contact us page. I will take a look for you.