Guess you are lucky. Many people here including me have hell lot of issues with Yahoo. haven't got it working at all. I have switched to Gmail now. Though they don't have the push its better than Yahoo.
I get days where it works perfectly, days where I can't even read or delete messages, and then in-between days, usually; where when I open the mail app, it continues getting push mail for a short while after I leave the mail app, otherwise working fine, then I imagine the garbage collector closes it down to free up the RAM the same way as it does the iPod and the browser. Yesterday was one of those perfect days. I never touched the mail app all day, but I was getting push.
Push mail is where an email you received is "pushed" instantly to you from the server when it is received whereas auto check on the iPhone checks at the time intervals specified. Currently, I believe only Yahoo push mail is supported on the iPhone.