The simple method for splitting an XLR cable is a basic "Y" adapter. Each of three wires within the cable is connected to two points. XLR cables provide protection from induced noise naturally, and this protects the signal through the split. Practically, one signal can be split two or three times before distortion and signal loss becomes significant. One potential drawback is a direct electrical connection between the mixers, though contemporary equipment does not typically show a problem.
The issue of direct connection between mixers is avoided through the use of transformer isolation in this style of split. The audio signal is induced between coils of the transformer, though any direct current voltage is blocked. The quality of the transformers used in this style of splitter has a crucial impact on the audio signal. Inexpensive transformers may not block induced noise or preserve the quality of the original signal.
While not directly related to splitter function, ground loops can occur when splitters are used. Each mixer will use the path of least resistance to ground. Usually, this is through the ground plug of each device, but many factors affect this, even when mixers are connected to the same circuit. Ground loops are noticeable by pronounced hum, usually noise-induced by current to ground routed somewhere it's not meant to be.
Microphones and mixers are a low-to-high impedance chain, by design. Splitting an XLR signal effectively reduces the impedance of the already low microphone impedance. This in turn causes the preamp of the mixer to work harder to create the same output. Potentially this raises the noise floor as well. With contemporary equipment, the boost needed can be split over several amplification sections, a process called "gain staging." In most cases, there will be no practical effect.