1D data
Let us take am example. Suppose we have a electrocardioagram i.e. the variation of voltage across the check as out heart beats. Each peak corresponds to one heartbeat. We could convolve this data with a filter in one dimension.
In a particular layer we can use multiple filters to have the output have multiple channels. All of the ideas of 2D convolution apply to 1D data.
3D data
3D data is a three dimensional input volume. Here is a example, if we take a CT scan which is a type of X-ray scan that gives a three dimensional model of your body. What a CT scan does is takes different slices through the body.
So if we want to apply a ConvNet to detect features in this three dimensional CT scan then we can generalize the idea from 2D convolution. The same principles apply here also.
If we have a input of size 14 x 14 x 14 and use filter of size 5 x 5 x 5 then we get a output of size 10 x 10 x 10. If we use 16 such filters then the output has 16 channels.