As @pierrecurie explained, one  reason to register the tensor as a buffer is to be able to serialize the model and restore all internal states.
Another one is that all buffers and parameters will be pushed to the device, if called on the parent model:
class MyModel(nn.Module):
    def __init__(self):
        super(MyModel, self).__init__()
        self.my_tensor = torch.randn(1)
        self.register_buffer('my_buffer', torch.randn(1))
        self.my_param = nn.Parameter(torch.randn(1))
        
    def forward(self, x):
            return x

model = MyModel()
print(model.my_tensor)
> tensor([0.9329])
print(model.state_dict())
> OrderedDict([('my_param', tensor([-0.2471])), ('my_buffer', tensor([1.2112]))])

model.cuda()
print(model.my_tensor)
> tensor([0.9329])
print(model.state_dict())
> OrderedDict([('my_param', tensor([-0.2471], device='cuda:0')), ('my_buffer', tensor([1.2112], device='cuda:0'))])

As you can see, model.my_tensor is still on the CPU, where is was created, while all parameters and buffers were pushed to the GPU after calling model.cuda().