'API Gateway' serves as a server that functions as the front-end of APIs, managing API requests, implementing throttling and security measures, directing requests to the appropriate back-end services, and relaying responses to the requestor. It operates as a reverse proxy, handling all application programming interface (API) calls, consolidating the necessary services, and delivering the correct outcome.

API Gateways establish a centralized, unified access point for various microservices, thus streamlining client-side programming. They typically manage overarching concerns like authentication, SSL termination, and rate limiting, relieving individual microservices of these tasks.

In microservices architectures, where a single client request may engage multiple services, the implementation of an API Gateway becomes crucial. It eases the client's workload by transferring the logic for interacting with numerous services from the client to the gateway, facilitating independent scaling of each component.

Contemporary API Gateways extend their functionalities to include API analytics, monetization, and developer workflow management. They are instrumental in API administration, ensuring governance, monitoring, and high availability of APIs.

To summarize, an API Gateway is a critical element in managing and directing API interactions, especially in intricate systems built on microservices architecture. It significantly contributes to the efficiency, security, and scalability of web applications, making it an indispensable tool in modern web development.