Distributed Antenna Systems (DASs) employ multiple antenna arrays in remote radio units to achieve highly directional transmission and provide great coverage performance for future-generation networks. However, the utilization of active antenna arrays results in a significant increase in hardware costs and power consumption for DAS. To address these issues, integrating DAS with Reconfigurable Intelligent Surfaces (RIS) offers a viable approach to ensure transmission performance while maintaining low hardware costs and power consumption. To incorporate the merits of RIS into the DAS from practical consideration, a novel architecture of ``Reconfigurable Distributed Antennas and Reflecting Surfaces (RDARS)'' is proposed in this paper. Specifically, based on the design of the additional direct-through state together with the existing high-quality fronthaul link, any element of the RDARS can be dynamically programmed to connect with the base station (BS) via fibers and perform the connected mode as remote distributed antennas of the BS to receive or transmit signals. Additionally, RDARS also inherits the low-cost and low-energy-consumption benefits of fully passive RISs by default configuring the elements as passive to perform the reflection mode. As a result, RDARS offers flexible control over the trade-off between distribution gain and reflection gain to enhance performance. The ergodic achievable rate under the RDARS architecture is analyzed and closed-form expression with meaningful insights is derived. The theoretical analysis and simulation results prove that the RDARS achieves a higher achievable rate than both DAS and RIS. A RDARS prototype with 256 elements is built for real experiments which shows that the RDARS-aided system can achieve an additional 21% and 170% throughput improvement over DAS and RIS-aided systems, respectively.