"higher intensity" and "high signal intensity" in images
The intensity of a pixel is its value (e.g., from 0 to 255).  For instance, in a black-and-white/grayscale image, pixel intensity 0 means the pixel is black, and pixel intensity 255 means the pixel is white; intensities in between the two are shades of grey.

"White matter lesions have higher intensity" means that the pixels in the area of a white matter lesion have higher intensity values.

In this context "signal intensity" is presumably a synonym for "intensity".