Your loop is all wrong; you are adding every listbox item to the same parameter name. And you never execute any command so nothing will go to the database. Your loop needs to take each ListBox item in turn, add it to the parameter set as you are doing, and then use
ExecutNonQuery
(as Maciej already told you), to send the item to the database.
queryString = "Insert into ServiceRecords([Personnel]) Values(@Personnels)"
command = New OleDbCommand(queryString, connection)
For i As Integer = 0 To Me.ListBox1.Items.Count + 1
command.Parameters.AddWithValue("@Personnels", ListBox1.Items(i))
command.ExecuteNonQuery()
command.Parameters.Clear()
Next
See
OleDbCommand.ExecuteNonQuery Method (System.Data.OleDb)[
^].