Spontaneous refers to something that is done or said in an impulsive, unplanned, or natural manner, without thinking or preparing in advance. It is an adjective that describes actions or reactions that occur instinctively, without any external influence or force. In the context of the novel "The Portrait of a Lady" by Henry James, the concept of spontaneity plays a significant role in the development of the characters and the overall plot.

Character Development:
1. Isabel Archer's Spontaneity: Isabel Archer, the protagonist of the novel, is portrayed as a spontaneous and independent young woman. Her decisions and actions are often driven by her desire for freedom and adventure, rather than societal expectations or conventions.
2. Ralph Touchett's Spontaneity: Ralph, Isabel's cousin, also exhibits a spontaneous nature. He is often described as someone who follows his instincts and acts on his emotions without much deliberation.
3. Madame Merle's Spontaneity: Madame Merle, a close friend of Isabel, is also characterized by her spontaneity. She is portrayed as a charismatic and impulsive woman who uses her spontaneity to manipulate and influence others.

Plot Progression:
1. Isabel's Spontaneous Decision to Reject Suitors: Throughout the novel, Isabel is presented with several marriage proposals. However, she consistently rejects them, opting instead for a life of independence and self-discovery. These rejections showcase her spontaneous nature and her desire to follow her own path.
2. Isabel's Spontaneous Trip to Italy: After inheriting a large fortune, Isabel decides to embark on a spontaneous trip to Italy. This journey serves as a turning point in the novel, as it exposes her to new experiences and influences that shape her future decisions.

Impact on Relationships:
1. Isabel's Spontaneous Friendship with Madame Merle: Isabel forms a close friendship with Madame Merle, who initially appears to be a spontaneous and exciting companion. However, as the plot unfolds, it is revealed that Madame Merle's spontaneity is a facade, and she has hidden motives.
2. Isabel's Spontaneous Marriage to Gilbert Osmond: In a moment of spontaneity, Isabel agrees to marry Gilbert Osmond, a manipulative and controlling man. This decision ultimately leads to her unhappiness and serves as a cautionary tale about the dangers of acting impulsively.

In conclusion, spontaneity is a crucial element in "The Portrait of a Lady." It shapes the characters' personalities, drives the plot forward, and explores the consequences of impulsive actions. The novel highlights the importance of balance and careful consideration in decision-making, cautioning against blindly following one's instincts without considering the potential consequences.