Take this example: Suppose that you have 3 PCs and on three seperate VLANs on switch-A, and have three servers on the corresponding VLANs on switch-B. Now if every PC on switch-A needs to speak to the corresponding server on switch-B, then you need to connect the two switches through ports that allow the three different VLANs (called trunk ports). Also, switch-A needs to tag any packet going out the trunk port so that switch-B knows to which VLAN this packet belongs (thus the use of tagging).

However, the two switches may agree that any untagged packet belongs to VLAN x lets say (keep in mind they have to agree on that). Keeping certain VLAN packets untagged is an option and may be useful in certain applications such as IP telephony when you have a PC connected to the IP phone where the phone understands tagged packets of VLAN Y and the PC on VLAN X doesn't understand the tagged packets.