Mapping an environment is essential for several robotic tasks, particularly for localization. In this letter, we address the problem of mapping the environment using LiDAR point clouds with the goal to obtain a map representation that is well suited for robot localization. To this end, we utilize a neural network to learn a discretization-free distance field of a given scene for localization. In contrast to prior approaches, we directly work on the sensor data and do not assume a perfect model of the environment or rely on normals. Inspired by the recently proposed NeRF representations, we supervise the network by points sampled along the measured beams, and our loss is designed to learn a valid distance field. Additionally, we show how to perform scan registration and global localization directly within the neural distance field. We illustrate the capabilities to globally localize within an indoor environment utilizing a particle filter as well as to perform scan registration by tracking the pose of a car based on matching LiDAR scans to the neural distance field.