Smalltalk adds to game lore and it is a means to acquire unique rewards:
Please follow the above links for details but in short:
- Trade Agents provide up-to-date information on trades at stations.
- Smalltalk discounts are different to other discounts so they are a stackable, additional option.
- You can ask for info on the better-skilled NPCs in the area.
- Virtual Seminars allow you to train one of your NPC's skills (addition of a star).
While <player> is docked on stations, NPCs will occasionally start talking, and when they do a speech bubble appears over their head to help identify them in a crowd.
This is the cue to undertake an optional minigame if we wish. There are quite a few conversation topics, from the mundane (eg chatting about holodancers) to the serious (eg concerns about messing with AI). Since they add colour to the game world, they can be interesting; unfortunately the discussions cannot be sped up or skipped and there are only a finite number, so in the end it is possible to get frustrated by them. This is where the 'Borderless Windowed mode' comes in handy as Alt+Tab to (eg) a website cuts the audio but lets you see how things progress, if you keep the website window clear of the subtitles. Similarly, while hunting for Smalltalk, you can do the same thing to pass the time while waiting for someone to start speaking. That's what I do anyway 
Finding smalltalk
As the chance of an NPC talking is random and not all NPCs will necessarily be the kind you would like to talk to, it is sensible to find a spot with lots of NPCs to increase the chance of a useful one talking early. Smalltalk is available only once per NPC; if you enter smalltalk then win, lose or cancel the 'talk, that NPC will not proffer smalltalk again until you leave the zone
Good places to find groups of NPCs:
- Bunk rooms on all docks tend to hold up to ~8 NPCs so smalltalk normally starts within 10-20 seconds.
- Generally, Administration platforms house permanent unhirable station crew, which can help when recruiting Trade Agents.
- A handy place is the Engineering platform as groups of NPCs tend to be right at the docking platform, although there tend to be fewer NPCs per dock
- In Albion or DeVries a good spot is the Trade platform since groups may hang around at the end of the first corridor.
- In Fields Of Opportunity|Verdant Profit|TU Overwatch, there are normally many Teladi in the main central docking area.
If you 'encourage' an NPC trader by selling something to them, or preferably buying something from them, the chance of them smalltalking appears to increase slightly. So hunt out those junk dealers & buy scrap metal from them personally if you're after a decent ship crew! Simply talking to an NPC can increase the chance of smalltalk happening, even if you only ask the way to another NPC.
Potential rewards from success* at:
level 1 smalltalk (numbers corresponding with radial menu):
- Ask for: Discount... (If NPC is a Trader they will offer a Personal discount for their wares (eg marines or rough gemstones) as well as a Station discount option (these are mutually exclusive); for all other NPCs the discount will apply to the (docked) station only - see below).
- -not used-
- Ask about: Job Applicant (offers the location and skills of a different NPC available to hire by <player> on the current dock). If no other hirable NPC exists this option will be unavailable
- Trade Updates (see below as not all NPCs offer it); they unlock continuous, real-time market info for the NPC's station. This does not have the same effect as posession of Trading Computer sofware.
- Give: Item... (give a craftable gift that unlocks level 2 of smalltalk).
- -not used-
Level 2 smalltalk (only available via the "Give: Item" option in level 1)
- Ask for: Discount... (a higher-quality version of the discount available at level 1 above)
- -not used-
- Ask about: Job Applicant (different to level 1 and 3 smalltalks, so perhaps the range setting is station or possibly a higher-lvl NPC will be offered? - needs checking)
- -not used-
- Continue: Smalltalk (hard) (unlocks L3 smalltalk)
- -not used-
Level 3 smalltalk** (only available via level 2 smalltalk option 5)
- Extended Discount. (lasts a long time; probably the same numerical discount as level 2)
- -not used-
- Best Job Applicant (offers the location and skills of an NPC of a chosen type with the best, previously unknown skills, in the Zone)
- Ask for: Employee training (a semi-predictable source of Virtual Seminars - see below)
- -not used-
- -not used-
* A score of 7+ or more across 2 or 3 minigames. 8+ is required across the first 2 minigames to access L2 smalltalk (if you require 3 games the L2 'Give..' option is disabled))
** A score of 4+ for all 3 minigames.
Location and skill visibility for hirable, well-skilled NPCs
These options only point to NPCs with unknown skills, so there could be other NPCs available to hire within range that won't be highlighted if their skills are already known. It makes sense to use these options where there are a lot of NPCs of the type you are interested in (e.g. see sidebar for zone-wide, or station dock menu to check platforms or station population).
More expensive hires are usually better skilled, but be aware that their cost is based upon their /total/ skill list, not simply the primary skills for their job.. so you could end up with a Captain who is rotten in Navigation and Leadership but excellent in Science & Management.. 
A useful point WRT hiring: find a station & target a dock. Then open the (I)nfo bar; you will now see all NPCs at all docks on the station. Find a suitable dock with <many> of the NPC type you wish to hire & dock there, using mission guidance if necessary. You can then smalltalk (to lvl1) any appropriate NPCs for free to discover the skills of the desired NPC; after that's done hire as necessary once their skills are known
NPCs randomly disappear from stations (but not docks if you're landed) to simulate personnel 'churn'. If you dock at one point & find a good NPC, don't expect them to remain there once you've docked at another point; leaving the zone will almost guarantee the NPC changearound*
*Specialists tend to hang on to their stations for quite a while; however there is still no guarantee they'll be there when you get back..
Collecting Virtual Seminars
Successful completion of the third smalltalk allows 'Virtual Seminars', which are easiest to come by via Smalltalk (they're now (v4) occasionally available via mission rewards or 'yellow ping' lockboxes too).
They are available for various potentially important skills, such as Engineering, Leadership and Morale: a Seminar can be used to add one star to the related skill of any one of your hired NPC's primary, bold-highlighted skills (eg only Engineering for Engineers, but Leadership or Navigation for a Captain), to a maximum of 5 stars. Exactly which Seminar you may be offered relates to the primary skills or the type of the NPC in question so it is somewhat random, in the sense that it is random as to which NPC may begin a smalltalk. Boarding experience for Marine Officers can only be gained through.. heh.. experience, and it's slow (around +(2d6+2)% at L4 per successful boarding), so be warned!
Seminars are only available through smalltalk after the Give (craftable) Gift option if the first smalltalk was completed with a score of 8+ points in 2 minigames and if the second minigame session was completed with a score of 4+ points in all 3 minigames. A higher (maximum?) score in the second minigame stage can increase the range (number) of seminars offered, depending upon the smalltalked NPC's class. <Player> can only pick 1 seminar as the prize, no matter how good the score.