How to bind list to dataGridView?

Use a BindingList and set the DataPropertyName-Property of the column.

Try the following:

...
private void BindGrid()
{
    gvFilesOnServer.AutoGenerateColumns = false;

    //create the column programatically
    DataGridViewCell cell = new DataGridViewTextBoxCell();
    DataGridViewTextBoxColumn colFileName = new DataGridViewTextBoxColumn()
    {
        CellTemplate = cell, 
        Name = "Value",
        HeaderText = "File Name",
        DataPropertyName = "Value" // Tell the column which property of FileName it should use
     };

    gvFilesOnServer.Columns.Add(colFileName);

    var filelist = GetFileListOnWebServer().ToList();
    var filenamesList = new BindingList<FileName>(filelist); // <-- BindingList

    //Bind BindingList directly to the DataGrid, no need of BindingSource
    gvFilesOnServer.DataSource = filenamesList 
}