It generally refers to window size for that filter.
For example, A gaussian filter with size=5 means a 5*5 gaussian matrix.
Generally, in discrete signal processing, filter size shows the window length. for 2D signals like image the window will be a matrix and for 1D signal like audio it is a vector.
Filtering is usaully applied to an image through convolution. The convolution kernell is a window (usually rectangle) which is slided over the image pixel by pixel (say from left to right) and replaces the middle pixel in the window by some kind of transformation which describes the filter (i.e. mean, median,...). The convolution widow may have differnt sizes ranging from 3x3, 3x5, 7x7,...21x21 pixels, even higher acording to the image/s or type of filtering you want to perform. The correct choice of the window size, as well as the iterations of the filter are crucial in the filtering process. Above operation is wel described in my book:
C.P. Loizou, C.S. Pattichis, “Despeckle filtering algorithms and software for ultrasound imaging,” Synthesis Lectures on Algorithms and Software for Engineering, Ed. Morgan & Claypool Publishers, 1537 Fourth Street, Suite 228, San Rafael, CA 94901 USA, June 2008, ISBN-13: 9781598296204.
as as in some other publications (please see C.P. Loizou et al IEEE TUFFC, 52(10):1653-1669, 2005; C. P. Loizou et al, Comp. Meth Prog. Biomed., 114:108-124, 2014.
Basically means the filter size... 5 means 5x5 element (kernel) for convolution. In general, larger kernels would remove more noise from the image. But they will also mean more undesirable artifacts as well. For an example, a 7x7 Gaussian would filter out more noise than a 3x3 Gaussian kernel... But they again, the 7x7 would blur out edges more. Its the same with many other filter kernels. So, you would have to compromise between the 2 and pick a size.
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