The syntax is C# and I wasn't sure if it was valid or not with VB. Basically what it does is create a new ClientAPI.ClientService.Client and set the FirstName and LastName properties based on the values you select. I think the following might be the correct VB syntax:

oClient = (From c
                 In oGeneric.GetClients()
                 Where c.Id = nClientID
                 Select new ClientAPI.ClientService.Client With { .FirstName = c.FirstName, .LastName = c.cLastName} ).FirstOrDefault()