Intelligent reflecting surfaces (IRSs) have been proposed as a promising technology to enhance signal transmissions in high-frequency bands. Up to now, the research on the performance of large networks with IRSs is still in its infancy. In this article, we study a Poisson bipolar network with line segment blockages and reflectors. By deriving the probability that an IRS can successfully reflect a signal from a transmitter to a receiver and the distribution of the distance traveled by the reflected signal, the performance impact of deploying IRSs on the signal propagation is investigated. The aggregated interference through reflective paths via IRSs is derived by modeling the IRSs as additional interfering sources with non-uniformly distributed interfering power in different directions. With these results, the signal-to-interference-and-noise ratio (SINR) and the achievable rate are further derived, where a characteristic function and the inverse theorem are adopted to handle the complicated channel fading of reflective signals. From the analysis, IRSs have a great potential to enhance the network performance, but the tradeoff between signal enhancement and reflective interference is important. That is, the performance gain suffers from a diminishing return with a large IRS fraction due to the growth of reflective interference.