There are a number of good reasons to do make a starter and I'll go through them as an abridged and extended version.
-Healthy yeast count
-Build necessary resources in the yeast to handle a wort
Some yeast in a pack you buy may be dead or at least weakened from its handling or age before you got them in your possession. You can outnumber the dead or weak ones by making a starter. A big beer will need more yeast in it than a smaller beer and we will get to that. This process will get you to the appropriate numbers.
Saccharomyces will put up with anaerobic environments but they would prefer to have access to oxygen. Their metabolism of sugar into usable energy yields at least 8 times more in the presence of oxygen than fermentation. The starter gives them the ability to eat down the sugars, build up energy (in the form of a phosphate compound called ATP), make glycogen (an energy bank), and build sterols critical to cell budding when you go anaerobic.
Your question regarding why it's needed because you are throwing them in a beer anyway is one I shared at one point as well. The answer as far as I've learned since is that the two conditions are very different. First there's oxygen, which we covered. Second, the starter gravity is very low. This is important because wort is very stressful on yeast. Osmotic pressure is created when the cells need to retain the water inside them but the density of wort around them pulls to create an equilibrium. They have to put in energy to just survive in a wort.
Lastly, there are far more cells per unit of volume in a starter compared to a batch of beer. Flocculation is a complicated process that is not well-understood but being able to bind with another yeast cell allows the culture to migrate around the wort and therefore munch through your beer efficiently. If you have too few cells that are in their prime you run the risk of a stalled fermentation, especially with high gravity brews.
Since others have mentioned keeping your starter going after high krausen, I'll chime in here too. I generally also let the yeast finish out in the flask before I chill and decant off the spent wort on brew day. The reason for this is when they are finishing up, they fill their glycogen banks that will get them through whatever fermentation you throw at them (within reason). I do pull cultures at high krausen however when I am keg conditioning.
When making starters, keep in mind yeast nutrient is important but doesn't cover all the needs of your yeast. They need vitamins and minerals not found in diammonium phosphate. I have taken to boiling 0.2-0.5 grams of dry yeast in the starter to add zinc and vitamin B's but you can buy products that do the same often sold as "energizers". I add both nutrient and energizer to starter and kettle.
