A synthetic oil filter is an oil filter that has synthetic filtering components inside it. These filters offer a higher degree of contaminant collection, in addition to providing less resistance to the flow of oil through them. Use of a synthetic oil filter is not a requirement just because your vehicle is using synthetic oil. However, under extreme cold conditions, a vehicle using synthetic oil would be better served by using this type of filter. Indeed, even though it costs more than conventional filters, use of a synthetic filter can be a benefit, regardless of the type of oil used.
For more info, see Synthetic Oil vs Conventional Motor Oil