The idea behind pulseaudio is live switching of streams. ALSA is great if you have only one audio card, but as soon as you introduce a bluetooth headset, a headphone, a HDMI display with sound output, ALSA can't handle real time stream redirection. Sure, you can use scripts to toggle .asoundrc profiles, but even then you'll need to restart the softwares that produce audio. Here I have a HDMI display (an hdtv) and a headphone. I mostly send my audio to my tv, but if I'm using the computer late at night, or if I'm to listen to high volume music, I'd switch the affecting streams to my headphone, without the need to mess with sound configuration files and to restart my sound engine.
PulseAudio is to audio what X.org is to video: stream mixing software.
