I don't really understand how the expansions/data packs work in android netrunner
Big Box expansions are deluxe expansions, those terms are synonymous. There are only 4 of these and they will always be tournament legal. Their structure focuses on specific factions (e.g., the first only pertained to HB and Shaper, with some neutral cards). 

Data packs come in "cycles" of 6 packs, which cover all the factions and have an overarching theme (usually in terms of story or mechanics).  We are currently on cycle 5 (the Mumbad cycle).  At some point in the future, the first two cycles will rotate out of competitive play but that won't be for at least a year or two. If you are just playing casually, this won't affect you.

No matter what you buy, you can find information on which cards are available in each pack online.  All packs should be available at your FLGS.

Unlike with some of FFG's other LCGs (e.g., for Lord of the Rings each deluxe expansion is necessary to play with the following adventure packs, but this is rare for the LCG model), in Netrunner you can pull cards from any expansion you want for your deck - so there is no need to buy everything unless you are a completionist (like many of us). This is what FFG meant in the above quote - you can play a Criminal deck without purchasing Honor &amp; Profit (the big box expansion that features Criminal cards) - however, in most cases, the big boxes yield some great cards and are worth the investment!

As a practical tip, you can browse netrunnerdb.com for decks, and when viewing one that strikes your fancy, click Sort above the decklist and choose "By Set".  That will tell you where all the cards for that particular list can be found.

Good luck and have fun!