You should always put a hosts into Maintenance Mode when you do reboots, firmware updates, apply ESXi updates (most patches require the host to be in Maintenance Mode) or anything like that. This will make sure all processes on the host are properly prepared, no VM will be (accidentally/DRS) migrated onto the host again, the HA agent is disabled etc.
Virtual machines that are running on a host entering Maintenance Mode need to be migrated to another host (either manually or automatically by DRS) or shut down. The host is in a state of Entering Maintenance Mode until all running virtual machines are powered down or migrated to different hosts. When host in Maintenance Mode, VMs cannot be created, powered on nor configured. Additionally, VMware vCenter Server will not migrate any VMs to this host while it is in Maintenance Mode. You can cancel the Enter Maintenance Mode task at any time.
So when you clicking enter Maintenance Mode it just initiates the task, and if you don't have any DRS you have to move all virtual machines manually to desired host. Once host is empty it will complete the task and will be pushed to Maintenance Mode completely.