WLED UDP Sync is the possibility to operate several WLED controllers in such a way that the connected LED strips on each controller are controlled synchronously and exactly the same way, i.e. always play the same color or the same effect by only setting this color or effect on one controller. You can also set what exactly needs to be synchronized: brightness, color, effects, segments, etc. In this way, several LED strips can show the same play of colors, even if they are connected to different WLED controllers for physical locations reasons, for example. The settings must be made in the "WLED broadcast" area under "Config->Sync Interfaces". Up to 8 groups can be defined. For example, you assign two controllers to one group and the other two to the other. Then the first two controllers are synchronized with each other (group 1) and the other two with each other (group 2), but not groups 1 and 2 with each other. On the main WLED user interface page there is a "Sync" button at the top that allows you to toggle WLED sync on and off. "UDP" in "WLED UDP Sync" means that this synchronization is implemented over a UDP network protocol.

In the Usermod "Audioreactive WLED" there is another sync that allows audio data to be sent from one WLED controller to others. The others can also react to the music without each having their own microphone or line-in adapter. This sync is implemented separately and is configured on the Usermod page.
WLED Sync uses what is known as multicast, whereby the data is sent from one sender to several/all receivers in the local network. Some modern WiFi routers consider it a kind of "disturbance" or "spam" on the network and either prohibit multicast immediately or suspend it after some time. If you have this problem, check your router's settings to see whether you can explicitly allow multicast (also look for broadcast, IGMP snooping or UPnP).