Convolutional neural networks (CNNs) have shown great effectiveness in medical image segmentation. However, they may be limited in modeling large inter-subject variations in organ shapes and sizes and exploiting global long-range contextual information. This is because CNNs typically employ convolutions with fixed-sized local receptive fields and lack the mechanisms to utilize global information. To address these limitations, we developed Dynamic Multi-Resolution Convolution (DMRC) and Dynamic Multi-Scale Convolution (DMSC) modules. Both modules enhance the representation capabilities of single convolutions to capture varying scaled features and global contextual information. This is achieved in the DMRC module by employing a convolutional filter on images with different resolutions and subsequently utilizing dynamic mechanisms to model global inter-dependencies between features. In contrast, the DMSC module extracts features at different scales by employing convolutions with different kernel sizes and utilizing dynamic mechanisms to extract global contextual information. The utilization of convolutions with different kernel sizes in the DMSC module may increase computational complexity. To lessen this burden, we propose to use a lightweight design for convolution layers with a large kernel size. Thus, DMSC and DMRC modules are designed as lightweight drop-in replacements for single convolutions, and they can be easily integrated into general CNN architectures for end-to-end training. The segmentation network was proposed by incorporating our DMSC and DMRC modules into a standard U-Net architecture, termed Dynamic Multi-scale and Multi-resolution Convolution network (DMC-Net). The results demonstrate that our proposed DMSC and DMRC can enhance the representation capabilities of single convolutions and improve segmentation accuracy.