"Stacking" switches have a few meanings related to how switches are interconnected. It might refer to a set of switches that have been cascaded or daisy chained (rather than a star configuration), or, switches connected by some "special" stack cable. When there's a "special" cable, there's generally some special features provided. The special features often provide more bandwidth then standard (Ethernet) ports, but more features might be provided.
In the case of the 3570 series you mention (also the 2750 mentioned by Leo), the dual stack cables provide a "32 Gbps" ring and allow the stack to function as one logical device. (Functionally, much like a chassis switch with line cards.)
Interesting features of the 3750 stack, vs. a chassis, you grow the "chassis" as you add individual stack units. (Unlike a true chassis where you need to select a specific model based on how many slots you think you'll need. BTW, there's a limit to number of 3750 stack memeber, which is nine.)
Also for the 3750 stack, one member unit functions much like a chassis supervisor and other units (internally) function much like line cards with on-board processing. If the current stack master fails, another unit will take over (much like having a redundant supervisor in a chassis). Each stack unit has it's own power supply, unlike a chassis whose power supply runs the whole chassis (unless it also provides a redundant power supply [NB: 3750 can be provided an external RPS for redundant power backup]).
With the 3750, you're able to build a stack, member by member (and as needed), that in many ways in much like a chassis. From a cost basis, stack members tends to be more (although often not much more) expensive than chassis line cards, but you don't need to purchase separate chassis, supervisor and power supply. (Usually a small stack is less expensive than a small chassis. A maximum stack might be more expensive than a like sized chassis.)
Functionally, a chassis might offer more features than a switch stack. Also, from a performance perspective, a chassis offen offers fabric bandwidth to each card slot while the stack is running across a ring.
(NB: BTW, it can be difficult to understand potential performance differences unless you really understand hardware. For instance, there are very important differences between Stackwise and Stackwise+ then just their nominal bandwidths, or within some chassis architectures. E.g. 6500 classic bus vs. CEF256 or CEF720, line cards with and without DFCs, 6513 vs. other 65xx, etc.)
At least on the 3570 series, configuration is rather automatic, but there are some "gotchas".
Perhaps the biggest pros for stackable switches are offen, but not always, less cost, less physical space, more flexible sizing. Biggest cons for stackables, might not be as feature rich, might not offer as much performance.
Stackables tend to be most interesting, I think, for LAN edge devices and L3 LAN distribution or core devices for smaller LANs.
