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In keyboarding parlance, staggering refers to the rows or columns of a keyboard being set offset to one-another.
Classic typewriter keyboard
The classic QWERTY typewriter keyboard layout has offsets between key rows, and the offsets are not the same. Thus, it is double staggered. The offsets are 1/2 key, 1/4 key and 1/2 key respectively.
The reason for this staggering was to allow equal distance between arms from each key to the type-writing mechanism.
There are also computer keyboards with an equal offset of 1/2 key. These days, most keyboards with this layout are point-of-sale keyboards. Vintage keyboards from the Eastern Europe often had this layout, as did several keyboards from Commodore, including the Commodore C128.
A symmetric stagger is a row-oriented layout organised into a left and a right half, for the left and the right hand respectively. On each half, the row offsets are the same and opposite of the other half.
Many "ergonomic" keyboards have instead keys organised in a columnar layout with offsets between columns. The offsets are most often not the same - if it was, then it would be equivalent to symmetric stagger.
Columnar layouts are sometimes called column-staggered
A keyboard layout with no staggering is called matrix layout or ortho-linear layout.