The main advantage is that you can use your receiver to select from multiple sources such as a satellite or cable box and a DVD player. With both the audio and video going to the receiver and then the video to the TV allows you to use the receiver to switch both audio and video at the same time.
In addition to what Lew said, some A/V receivers will also upconvert from composite or S-video to component/HDMI, so you can have any source going to the receiver and only one set of cables going to the TV. This is usually present in the mid to high priced receivers.
My advice if you are on strict budget is to buy a 5.1 receiver (and two fewer speakers). Use your money to buy higher quality components rather than two extra channels that were in most cases not present in the theater presentations in any case.
I wouldn't look at a reciever for upconverting capability. Depending on your other components, your DVD player, your TV... my already do this, and may do it better. I don't know if recievers will upconvert to HDMI, mine doesn't. My DVD player on the other hand will not upconvert via anything but HDMI. Simple answer is, the receiver is there to process audio and switch video for convienence, and yes, converting the lesser signals to Component is nice, I don't think it improves the picture quality.