A unified neural network model consists of one neural network as opposed to other models that rely on two or more neural networks.
For example, from page two of the YOLO paper:
2. Unified Detection
We unify the separate components of object detection into a single neural network. Our network uses features from the entire image to predict each bounding box. It also predicts all bounding boxes across all classes for an image simultaneously. This means our network reasons globally about the full image and all the objects in the image. The YOLO design enables end-to-end training and realtime speeds while maintaining high average precision.
In the paper by Xu and Wang, they add a branch to handle tracking to the Faster R-CNN architecture, which was designed for object detection. This is a 'unification' of two models.
In the paper by Ebrahimi et al., on pages 42-43, you can see they are fusing multiple neural networks into one unified model:
We propose a unified user geolocation method that relies on a fusion of neural networks, incorporating different types of available information: tweet message, users' social relationships, and metadata fields embedded in tweets and profiles.