One of the central conflicts which we see in this novel is the conflict of imagination pitted against social expectations. This is an external conflict, but also internal, and we see the forces of imagination most clearly in Anne. The forces of imagination often lead Anne away, distracting her from her household duties. Although Anne is pleased by the power of her daydreams, her powerful imagination brings her into conflict with the expectations of the Avonlea community. Marilia definitely does not share Anne's romantic sensibilities, and thus is exasperated by her continual disasters: cooking a cake that cannot be eaten or nearly drowning herself to act out a poem. This conflict is resolved as the novel progresses as Anne finds the ability to moderate her romanticism and strike a balance between her imagination and social respectability.
Another obvious external conflict is the animosity between Anne and Gilbert. The function of this conflict is to spur them both on to greater academic achievements, and it is a testament to the stubborness of Anne's character that she is only able to speak to Gilbert towards the end of the novel.