Zombies come from the East and North and the Siege lasts for two waves. Everything from ordering an airdrop full of supplies, to asking a fellow soldier to accompany you, to repairing melee weapons runs on it. The stars basically represent dollar signs, just think of it that way. If you don’t have a high enough influence to complete the chosen action, the character will refuse to do it. Influence is the main “currency” of Lifeline.
Also, you might not always have enough Influence to order a supply drop, so every little item counts toward making your life easier in that regard. Besides, when you Establish Outposts (more on that in a minute) you can find useful things in these spots. You can order supply drops rather than go out and hunt for supplies, but in my opinion that takes some of the fun out of it. Of course, you also need to take on groups of the undead, but you are a military unit and have the equipment and connections to make this task simple. Like the main State of Decay storyline, you will need to scavenge for supplies and protect your base.