Basics
Being extremely fragile compared to other dedicated melee troops, banshees should usually disregard this type of troop, and instead focus ranged units, as their power melee lets them engage even Tactical Space Marine squads without leaving them exposed to counter-attacks for too long (thanks to their melee type reducing the passive 40% melee resistance effect of this squad).
They, however, should avoid anti-melee units (Unupgraded heretic or shotgun scout squads, for example) as much as possible, as they abilities will heavily damage and supress the Squad, thus leaving them open to ennemy fire. If such a thing happens, and depending on the circumstances, your best bet will usually be to retreat the squad (assuming that there are no ennemy melee units on the retreat path) before losing more models.
Their abilities also play a huge role for them, as fleet of foot will let the Squad get in reach of their target even faster, as well as Reduce ranged damage taken by 50% once upgraded with their Exarch, and their scream, paired with the former ability, will make them able to supress multiple squad (note that as long as the banshees are screaming, they will supress any infantry that comes near them, which means that you can move them around to maximize its effect), thus limiting the damage they will take from other ranged units, or slowing down ennemy melee squads on their path.
Anti-Vehicle capabilities
Once upgraded with the aspect of Banshee, the Banshee exarch replaces her mirror swords with and Executioner, this will be your primary source of anti-vehicle damage, as it is the only weapon that can effectively penetrate the vehicle's armor. This makes the squad a threat to enemy light vehicles as well as tanks (although the damage against the latter will be more limited), however, the squad still retains its fragility and should always be watched over to avoid a wipe.