As mentioned in the wiki article, convolutional layers are optimized for translationally-invariant parameters, such as pixel intensities in images and video. If your parameters represent a discretized sample of a continuous variable, such as space or time, then translational invariance means that every window of the parameters (such as a 10x10 pixel slice of the image) is to some extent similar to every other and benefits to be pre-processed (filtered) by the same means. In this case, you can select a convolutional layer, and by doing so, enforce your knowledge about the symmetries of this world onto your neuronal network.
On the other hand side, if you have a bunch of input parameters whose indices are not related to their meaning (e.g. params=[temperature, pressure, volume, loudness, brightness, ...]), then they are most certainly not translationally-invariant, the intrinsic assumptions of the convolution layer are not met, and it is only detremental to use it