Intelligent reflecting surface (IRS) is a promising technology to reconfigure wireless channels, which brings a new degree of freedom for the design of future wireless networks. This article proposes a new three-dimensional (3D) wireless system architecture enabled by aerial IRS (AIRS). Compared to the conventional terrestrial IRS, AIRS enjoys more deployment flexibility as well as wider-view signal reflection, thanks to its high altitude and thus more likelihood of establishing line-of-sight (LoS) links with ground source/destination nodes. We aim to maximize the worst-case signal-to-noise ratio (SNR) over all locations in a target area by jointly optimizing the transmit beamforming for the source node, as well as the placement and 3D passive beamforming for the AIRS. The formulated problem is non-convex and difficult to solve. To gain useful insights, we first consider the special case of maximizing the SNR at a given target location, for which the optimal solution is obtained in closed-form. The result shows that the optimal horizontal AIRS placement only depends on the ratio between the source-destination distance and the AIRS altitude. Then for the general case of AIRS-enabled area coverage, we propose an efficient solution by decoupling the AIRS passive beamforming design to maximize the worst-case array gain , from its placement optimization by balancing the resulting angular span and the cascaded channel path loss. Our proposed solution is based on a novel 3D beam broadening and flattening technique, where the passive array of the AIRS is divided into sub-arrays of appropriate size, and their phase shifts are designed to form a flattened beam pattern with adjustable beamwidth catering to the size of the coverage area. Both uniform linear array (ULA)-based and uniform planar array (UPA)-based AIRSs are considered in our design, which enable two-dimensional (2D) and 3D passive beamforming, respectively. Numerical results show that the proposed designs achieve significant performance gains over the benchmark schemes.