Final answer:
The Kaaba is influential in Islamic architecture as it determines the orientation of the qibla wall in mosques, which contains the mihrab pointing towards Mecca where the Kaaba is sited.
Step-by-step explanation:
The Kaaba proved influential on later Islamic architecture primarily because it serves as the orientation for the qibla wall in all mosques. Every mosque contains a mihrab, a niche indicating the direction of Mecca, which is known as the qibla. Since the Kaaba is situated in Mecca, the mihrab in every mosque points toward it, and thus it directly influences all Islamic places of worship. The qibla wall, often the most elaborately adorned part of a mosque, signifies the direction for Muslim prayers, regardless of the mosque's geographic location.
In addition to the qibla, the physical design of the Kaaba—a cube-like structure—has set a precedent for the use of simple, geometric forms in Islamic architecture, which contrasts with the intricate decorations often found inside mosques. Further, the Kaaba has been a center for Islamic pilgrimage since Muhammad purged it of idols and rededicated it.