The smack packs only come with about 100 billion yeast cells. That's not enough to ensure a healthy fermentation if you're doing a 5 gallon batch over 1.050 starting gravity. See Mr. Malty's pitching rate calculator:
http://www.mrmalty.com/calc/calc.html
Making a yeast starter is a technique to replicate yeast. You're essentially making a mini beer, but you'll want to make this mini beer a low gravity (1.040), as to not shock the yeast (see osmotic shock). We also tend to add yeast nutrients so that it promotes healthy growth and not just a way to ferment sugar. Many people will constantly aerate it (see stir plate), to promote more/faster growth.
The key advantages:
- You're pitching enough healthy yeast to do the job adequately
- You're sure the yeast is actually healthy because you've observed the starter activity
- Fermentation takes off in no time at all (no worrying and posting questions about your yeast all weekend).
I like to do my starters a week in advanced. This gives me 3 days to allow for growth. Then I'll pop it in the fridge for 3-4 days to allow the yeast to flocculate to the bottom. Then, I can decant (pour) off the top half of the starter (get rid of that flavorless, oxidized beer) and pour the rest right into my new batch of beer.
John Palmer describes the process very well:
http://www.howtobrew.com/section1/chapter6-5.html
Also, if you want to listen to podcasts on the subject, Jamil and John do one on the Brew Network and they have a great episode on yeast starters.