I saw a picture of a network-structure with VLANs in it:
Why would somebody structure their network like this? Does this even make sense? I mean, they are in a different LAN, why then mapping a VLAN to each one?
Using VLANs is like breaking a switch into multiple unconnected switches. On a single switch, no hosts on a VLAN will ever see any traffic for a different VLAN. Traffic must pass through a router, where it can be controlled, to get from one VLAN to a different VLAN.
There are many reasons to use VLANs. One is that switches will flood unknown unicast traffic, and broadcast and multicast traffic is sent to all the other interfaces. Someone with bad intentions could be snooping on that traffic for other networks if the switch wasn't broken into VLANs. With VLANs, that type of traffic is restricted to interfaces configured for the VLAN.
Generally, network virtualization allows your network's logical structure to become largely independent from its physical structure.
VLANs allow you to segment your network in any reasonable way, no matter where the nodes are physically connected. In your diagram, there is a functional segmentation that is completely independent from the physical connectivity - absolutely valid and reasonable when the separation is required.
Instead of using dedicated segment switches on each floor and running each uplink separately, VLANs allow you to aggregate (trunk) the uplinks and use a single switch (or fewer switches) for horizontal floor distribution.
With additional meshing features like MSTP or RPVST this becomes even more attractive and resource-saving.