A regularization parameter is a parameter used in some Non Linear Iterative Methods to suppress undesired solutions, by penalizing those with very high spectral frequencies that account for rich small-scale structure.
The Huygens Software uses a regularization parameter in some of its Restoration Methods that is a function of the inverse Signal To Noise Ratio: the lower the entered SNR, the higher the regularization parameter, and the more the solution will be constrained into the smooth range. Like that, noise amplification is prevented that would generate fake small-scale structure.
Suppose, as an example, that you want to do Image Restoration by minimizing the squared difference between the recorded image and a blurred estimate of the original object (this is, the estimate convolved with the Point Spread Function PSF). But in this last step, in the convolution, the PSF acts as a Cookie Cutter supressing all the high frequencies of the estimate, so they are not taken into account in the minimization. At the end you may find an estimate that is good in the low frequency region, but that is totally nonsense in the high frequencies, that are basically dominated by noise. A Regularized Method uses the regularization parameter to penalize solutions that oscillate too much, i.e., with a look of small-scale structure.