A convolution with a 3×3 kernel: at each position, multiply the 9 kernel values with the 9 underlying input values and sum them. This produces one output value. Slide the kernel to the next position and repeat. A single kernel produces one feature map (detecting one pattern). Multiple kernels produce multiple feature maps. Stride (how far the kernel moves each step) and padding (how to handle edges) are additional parameters that control the output size.
In a CNN, early layers use small kernels to detect simple patterns. Each subsequent layer convolves over the previous layer's feature maps, detecting progressively more complex patterns. Layer 1: edges. Layer 2: corners and textures (combinations of edges). Layer 3: object parts (combinations of textures). Layer 4: objects (combinations of parts). This hierarchical feature learning is the fundamental mechanism behind CNNs' success in vision.
Convolutions aren't limited to 2D images. 1D convolutions process sequences (audio waveforms, time series, text), sliding a kernel along one dimension. 3D convolutions process volumes (video, medical scans), sliding along three dimensions. The principle is identical: local pattern detection with parameter sharing. 1D convolutions are used in some modern architectures (ConvNeXt, Hyena) as efficient alternatives to attention for certain operations.