For "Sign Up," there is a checkbox for, "Require administrator approval for sign ups." When this box is checked, all employee shift sign-ups remain pending until an administrator approves the request. This is an excellent option for when you aren't exactly short on employees looking to pick up a shift and you want to decide from a list of people who have bid for the shift. I should mention that "Work Limits" rules apply here so if an employee is over their weekly hourly quota, he or she wouldn't be able to sign up for a shift anyway.
Deselecting this option means that as long as your employee is still within your defined work limits, he or she will be scheduled for the shift based on first come, first serve. What if you want shifts to be first come, first serve for awhile and then have them manually approved? Help yourself! There's nothing stopping you from setting your sign up setting to not require approval and then set it to require approval later!
For "Trades/Giveaways," same concept applies. When "automatic" is selected for Trade/Giveaway Approval, any trade/giveaway, within your defined work limits, will be processed automatically without requiring an administrator's approval.
These settings are available to you to give you flexibility in managing your scheduling change requests. If you are a volunteer business and are looking for people to pick up shifts, automatic approval is the way to go. If you are a business where your employees are fighting over any open shifts, I'd go with manual approval.