Cross-section is actually a probability which determines if a nuclear reaction takes place. This probability depends, among other parameters, on the energy of the incident particle, neutron in this case. An interpretation of cross-section for thermal neutron is the interaction of partial waves (quantum mechanics point of view) with a plane wave. You do not forget that this is only one description. Also you should not forget the resonances, something that happens and could be well described by partial waves. Again: it is only a description. Waves describe and permit to calculate parameters of physical events. You can also try to describe the physics of thermal neutron capture through semi-classical approaches, doesn't matter. The main thing is, that you have very clear the concept of cross-section, its definition. How you calculate it, is secondary part of the problem.
Agree with Moreira. Lower the velocity of the neutron, more time it will spend around a given nucleus and more will be the cross-section. plot lamda=h/mv. Somewhat crude trend, 1/x type graph
Could you please be a little bit more specific. Why Boron-10 has larger cross-section for thermal neutron than Boron-11? Similarly, the cross-section of thermal neutron for Uranium-235 is much larger than Uranium-238......