Sand dune flora perform many functions, but perhaps the best known is dune stabilization. Sand dunes are very prone to erosion from winds and storm waves; the rhizome and root systems of plants, especially grasses, can reduce the mobility of sand and consequent damage to the dunes themselves and to human and other terrestrial communities behind the dunes. Woody bushes and trees that can survive dune environments can engender a unique "maritime forest" habitat in old, well-developed dune fields with their own unique plant and animal communities. These more robust systems provide yet more protection from storms for humans and other terrestrial systems behind them. The Atlantic coast of the U.S., where ocean storms are an ever-present hazard, provides a lot of positive examples of this, where preserved vegetated dunes have protected towns from storm winds and tides, as well as many negative examples where lack of dunes, and in particular vegetated dunes, have led to severe damage. This is widely recognized and in many places it is illegal to build over or in front of dunes and local laws even prevent people from walking over dunes in order to prevent damage to dune vegetation from foot traffic.
One might add that e.g. the German and other sand dune islands would not exist without plant colonisation in an early stage of succession.
Early colonisers like Elymus farctus stabilise the primary dunes and allow the next stages of succession to establish: secondary dunes, followed by tertiary dunes (grey dunes). Each of these stages of succession enables new species (e.g. many different insects) to colonise the newly built habitats.
I think that the sand dune flora reduce the aeolian transport of sand, and increase the consolidation rates of sand dune. It allows the development of the dune.