Zigbee is a specification for a suite of high level communication protocols used to create personal area networks built from small, low-power digital radios. ZigBee is designed for things like home automation, medical device data collection, and other low-power, low-bandwidth needs. ZigBee is a low-power, low data rate, and close proximity (i.e. personal area) wireless ad-hoc network.
ZigBee and Wi-Fi both use the 2.4GHz band but they have different channel numbers and bandwidths. With care it is possible to configure them to co-existence nicely, by completely avoiding channel overlaps. It is usually it is the lower power ZigBee mesh that is impacted most by the higher power Wi-Fi signals. Both use Clear Channel Assessment (CCA) to check if the channel is clear before an attempt to transmit. If there are channels overlapping, then provided there are gaps in data transmissions both can work, but with reduced throughput. However, if your WiFi is using very high data rates (perhaps while streaming video) there will be few gaps for an overlapping ZigBee mesh to use.
Since ZigBee data rates are very low the transmission is not continuous, so there are frequent gaps that can be used by other ZigBee mesh networks that occupy the same ZigBee channel. In practice you can have multiple ZigBee (or other 802.15.4 based radios, such as Thread) using the same channel, provided they are not overlapping with a higher power Wi-Fi channel.
Wi-Fi routers and Access Points often default to use auto channel selection, to select the least congested Wi-Fi channel and avoid interference from other nearby Wi-Fi networks. Unfortunately, they do not detect ZigBee signals and so it is impossible for them to avoid overlaps with any ZigBee mesh networks that might be present.
It is often better to assign (fix) the Wi-Fi channel to be 1, 6 or 11, as this will ensure there are gaps for a ZigBee mesh to use. Many ZigBee hubs also use auto channel selection to find such gaps, but some have manual selection. For example, the Philips Hue Bridge can be manually set to one of four ZigBee channels 11, 15, 20, or 25. (Channel 26 is also available in some countries but in the USA it has to run at reduced power so it is not the best choice there).
Be aware that 2.4GHz Wi-Fi channels are 20MHz wide by default, but the higher speeds possible with 802.11n and 802.11ax use use 40MHz wide channels, which reduces the possible gaps for ZigBee.
