What does overhead rate mean? In US, universities often have a fixed overhead rate around 50%, or at least that's what I heard. But I don't know what it exactly means. How does this affect how much grant money goes where?
The 'overhead' generally refers to the funding that doesn't go directly to research expenses (salaries of researchers, cost of experiments/consumables, etc) but to the supporting expenses (salaries of administrative/support staff; cost of facilities and utilities, equipment depreciation) of services that are neccessary but not directly related to research.

It often is set by university administration to some fixed rate (50% sounds high to me, but it depends on country and research domain) that is taken from all grants and used to fund those 'common' expenses.