You can travel around 'grid' at conventional speeds where most of the interesting action takes place, you can warp from one grid to another inside a solar system, and you can jump from one system to another via jump gates/portals/bridges or wormholes. In some situations you can fly from one location in system to another without warping depending on the distance, your ship's speed and your patience, it's quite possible to build ships that exceed 10km/sec without running out of cap, and there are some stations that are thousands of kilometers apart, there are occasionally reasons to do this kind of thing - generating bookmarks and some fancy grid-fu. However distances inside solar systems are generally measured in Astronomical Units, which in layman's terms is loosely defined as the distance from the Earth to the Sun, 1AU is roughly 150 million kilometers so you'd take a good 6 months to move this far in your speed setup.
So, warp drive is what we use, even the crappy rookie ships can travel around at 3AU/second, that's 1.6 billion billion kilometers per hour, 1500 times the speed of light, so you can cover most distances inside solar systems in under a minute, some ships are even faster than this, but it's rare that it makes a significant difference. The thing about warp drive is that you need a known destination, you can't just point your ship at the second star on the left and go straight on until morning, not least because 'morning' is a hugely subjective term when you're not tied down to the surface of a planet. The game let you warp to known celestials like planets, moons and asteroid belts, your agents will supply you with bookmarks for mission objectives, and you can scan down the locations of some things using probes. If you're part of a fleet you can warp to other pilots in the fleet, which can be a really bad idea if you don't check with them first and find yourself in the middle of a hostile battlefleet that your cloaked associate was observing.
I'm sure you know that you can make bookmarks any time for later use, and the traditional method of creating 'safe spots' is to make a bookmark when your warping between some planets. They're called safe spots because bad guys can't find you there by accident, they have to break out the probes and scan you down, and even then it's possible to cloak your ship or reduce it's scan signature enough to make it invisible to probes. This well known method lets you generate a hard to find spot inside the solar system, however, there's a technique which lets you exploit the emergency warp mechanics and get safe spots anywhere, and with enough effort you an generate a spot 1000+AU from the star.
These super deep safes are important strategic resources because moving capital ships around doesn't work using jump gates like everyone else, capital ships have their own jump drives that propel them instantaneously from one system to another. But such epic feats of navigation are not possible without a cynosuaral beacon, a device that sends a powerful signal that a capital ship can lock onto and jump to, unfortunately it's so powerful that everyone in that destination system sees it, and they can warp to it. Worse, the beacon when activated stays activated for several minutes, and immobilises the host ship making it a sitting duck with a huge flashing sign saying 'here's a sitting duck'. Capital ships are also not known for their agility, once they arrive at their destination they take a long time to get into warp, it's easy for a hostile force to respond to a cyno beacon and tackle whatever is coming through. Super deep safespots buy the incoming fleet time to warp off to another spot before any hostile forces can intercept which is generally considered 'a good thing (tm)'.
So now I've explained all that I'm sure you want to know all about this exploit, well I'm not explaining it again, there's a whole bunch of other places that explain the tricks. The goons published a guide called 'project poseidon', although they recommend using an Anathema, I found that it's more efficient to use a Blockade runner with Hyperspatial Velocity Optimization rigs, and in friendly territory Hulks and Orcas are better still.
Anyway this is no longer the big secret it once was, CCP have decided to fix the 'problem' and so if you try to use the 'logging out in warp' trick on Singularity you'll find that the ship completes the regular warp cycle first before it initiates the emergency warp. No more shall you be able to create these bookmarks beyond the edge of the system. And now there's a question about the bookmarks that already exist, will CCP delete these? Or will they become something of a shadowy commodity increasingly valuable over time as old players leave and take their bookmarks with them?