Slices in Sketch App are in fact the same concept as slices in Affinity Designer, or in Adobe Illustrator - they combine a way to select a particular area of a design as being exportable as a separate graphic entity, and a type of "bucket" for holding one or more specific export settings that relate to how that specific area is to be exported.
You design a UI (User Interface) for a website using Sketch.
You design the entire page, give it constraints to make it responsive, set breakpoints, go through the interactivity setup to allow your mockup to be click-throughable... then you set up slices, which define areas of export.
You slice up the whole design so that you get a header, navigation bar, body area, and footer, and in addition you sub-slice all the icons and buttons individually. The header and footer you choose to export as say .pngs, at three different scales, and also as a single .svg just in case. You choose to export your body area as three .png as different resolutions, but in this case as the body background has a screened photographic image, you choose not to do an .svg. The buttons and icons you choose to go with just .svg, because you know you have enough skill with CSS to recolour them live in the final design, and you suspect there will be a need for this.
Because you've been careful in how you set up your slices, you now have one click batch export of everything; more crucially, this will continue to be the case even as you iterate the design through multiple rounds of client review sessions, and one last time when you have to iterate slightly to work with the backend coder the client has suddenly chosen to assign - that coder is super happy to be receiving consistent output from you, and later when asked to recommend a designer, happily mentions how reliably easy you are to work with.