Whats this image you have uploaded? In what context is it about sliver polygons?
Yes, those polygon "islands" are the slivers
As Duncan says, 'sliver' is not the right terminology.
Without seeing the rest of the data, I would suggest selecting you main land body and then using select by location to select all features intersecting and within it.
Export your selection to a new feature, or switch selection and delete.
Hi Jota Us,
If your data is projected you could do a selection by Shape area greater than the "sliver" Island polygons, therefore selecting only the polygons you wish to keep and export the selection to a new feature. Preserving your original data. This also assumes that all the "slivers" are smaller in area than your study area.
Shane