Future Internet-of-Things (IoT) will connect billions of small computing devices embedded in the environment and support their device-to-device (D2D) communication. Powering this massive number of embedded devices is a key challenge of designing IoT since batteries increase the devices' form factors and battery recharging/replacement is difficult. To tackle this challenge, we propose a novel network architecture that enables D2D communication between passive nodes by integrating wireless power transfer and backscatter communication, which is called a wirelessly powered backscatter communication (WP-BackCom) network. In the network, standalone power beacons (PBs) are deployed for wirelessly powering nodes by beaming unmodulated carrier signals to targeted nodes. Provisioned with a backscatter antenna, a node transmits data to an intended receiver by modulating and reflecting a fraction of a carrier signal. Such transmission by backscatter consumes orders-of-magnitude less power than a traditional radio. Thereby, the dense deployment of low-complexity PBs with high transmission power can power a large-scale IoT. In this paper, a WP-BackCom network is modeled as a random Poisson cluster process in the horizontal plane where PBs are Poisson distributed and active ad-hoc pairs of backscatter communication nodes with fixed separation distances form random clusters centered at PBs. The backscatter nodes can harvest energy from and backscatter carrier signals transmitted by PBs. Furthermore, the transmission power of each node depends on the distance from the associated PB. Applying stochastic geometry, the network coverage probability and transmission capacity are derived and optimized as functions of backscatter parameters, including backscatter duty cycle and reflection coefficient, as well as the PB density. The effects of the parameters on network performance are characterized.