There are basically 2 different ways to INSERT records without having an error:
1) When the IDENTITY_INSERT is set OFF. The PRIMARY KEY "ID" MUST NOT BE PRESENT
2) When the IDENTITY_INSERT is set ON. The PRIMARY KEY "ID" MUST BE PRESENT
As per the following example from the same Table created with an IDENTITY PRIMARY KEY:
CREATE TABLE [dbo].[Persons] (    
    ID INT IDENTITY(1,1) PRIMARY KEY,
    LastName VARCHAR(40) NOT NULL,
    FirstName VARCHAR(40)
);
1) In the first example, you can insert new records into the table without getting an error when the IDENTITY_INSERT is OFF. The PRIMARY KEY "ID" MUST NOT BE PRESENT from the "INSERT INTO" Statements and a unique ID value will be added automatically:.  If the ID is present from the INSERT in this case, you will get the error "Cannot insert explicit value for identify column in table..."
SET IDENTITY_INSERT [dbo].[Persons] OFF;
INSERT INTO [dbo].[Persons] (FirstName,LastName)
VALUES ('JANE','DOE'); 
INSERT INTO Persons (FirstName,LastName) 
VALUES ('JOE','BROWN');
OUTPUT of TABLE [dbo].[Persons] will be:
ID    LastName   FirstName
1     DOE        Jane
2     BROWN      JOE
2) In the Second example, you can insert new records into the table without getting an error when the IDENTITY_INSERT is ON. The PRIMARY KEY "ID" MUST BE PRESENT from the "INSERT INTO" Statements as long as the ID value does not already exist: If the ID is NOT present from the INSERT in this case, you will get the error "Explicit value must be specified for identity column table..."
SET IDENTITY_INSERT [dbo].[Persons] ON;
INSERT INTO [dbo].[Persons] (ID,FirstName,LastName)
VALUES (5,'JOHN','WHITE'); 
INSERT INTO [dbo].[Persons] (ID,FirstName,LastName)
VALUES (3,'JACK','BLACK'); 
OUTPUT of TABLE [dbo].[Persons] will be:
ID    LastName   FirstName
1     DOE        Jane
2     BROWN      JOE
3     BLACK      JACK
5     WHITE      JOHN