撑腰 literally means 'to prop up the waist', but it's almost always used figuratively to mean 'to back someone up' or 'to provide support' — especially from a person in a position of power or authority. It's a separable verb (离合词): you can insert elements between 撑 and 腰, such as 撑他的腰 ('back him up'). The support is usually active and involves giving someone confidence or protection.