A fat tree topology "ensures" bandwidth by utilising thicker links closer to the core or root, compared to a normal "skinny" tree where you have the same links everywhere.
So for an example, imagine that you have a network with access, distribution and core layers. The 4 access switches each connect 4 hosts using 1 GigE and you're designing a fat tree. The access switches connect to 2 distribution switches which are connected to a single root switch.
For a fat tree, designed 1:1, you'd make sure that the access <-> distribution trunks are 4 GigE, and the core <-> distribution trunks would need to be 8 GigE.
As you can see, you're not ensuring anything, you're just making sure that along every path of the network, every host has it's own 1 GigE of bandwidth.
Here's a good article if you want to learn more;