All this data is potentially out of date, and should be taken with a truckload of salt
Little more than armed shuttles, rookie ships are the basic tech I frigates that new pilots start with, and that are given free of charge to any pilot who docks his pod at a station he has no ships at.
Rookie ships spawn with a civilian mining laser and a race-specific civilian weapon already fit, and a single unit of Tritanium in the hold. The initial rookie ship a new player receives will also have a Damage Control I fit, unless the player lacks the skills to fit it, in which case it will be placed in their hangar.
Rookie ships can be sold both on the market, contracts and through the trade window.
Common Non-Rookie Uses
Mining Operation Harassment and Piracy
The Velator and Ibis are both capable of dealing significant DPS while tanking poorly-skilled drone and missile fire, making them ideal for harassing high-security mining operations as many miners will see a rookie ship and dismiss it out of hand, making them far more likely to engage the would-be pirate.
Well skilled and flown ships of these types are capable of taking down mining cruisers, and even Retriever mining barges, so long as the pilot does not possess high drone skills, though Hulks and the odd mining battlecruiser or battleship are well beyond even the best pilots skills when in a Velator or Ibis.
Though not a 'serious' fit by any stretch, doing level one missions or level one or two plexes in rookie ship can be a fun challenge for an experienced pilot. Even lowsec ratting is possible, given a competent pilot and a good fit.
Rookie Ship Hulls
You can get these ships by joining CCP at one of their many events around the world or by trading for/buying it in game.