I did not understand the necessity of the "while " statement and the statement "if player:" in this code

I did not understand the necessity of the "while " statement and the statement "if player:" in this code -

def get_players_list():
    """() -> list of [str, int] list

    Prompt the player(s) to enter their names and return a list of player info
    as a two-item list with name and score, respectively.
    """

    players = []
    player = input('Enter player 1 name: ')
    while player.strip() or not players:  ##**#why is this needed?**
        player = player.strip() 

        if player in players:
            print("A player by that name is already playing.")

        if player: **# what is the function of this command#**
            players.append([player, 0])

        if players:
            print('Leave a blank player name to begin playing.')
        player = input('Enter player {num} name: '.format(num=len(players) + 1))

    return players