Legibility is, simply put, how easy it is to find your way around in a transit system, how easy it is to look at a part of a transit network and figure out what vehicle will take you from where you are to where you need to go. Our bus network does a terribly bad job of it out here. I was in the midst of writing a post on the to/via problem in naming transit routes in Riverside, and I was under the impression that most bus lines in Riverside run primarily along one or two arterial streets through the city. This is true, if you only look at the portion of the routes that run between Downtown and the Galleria at Tyler (which is where I spend most of my riding time), but when trying to propose names for our routes based on the streets they travel on, I found myself struggling. The 1 and 15 are pretty straightforward routes, but take a look at the 10. My mental impression of this route is that it's relatively simple, but try to come up with a description of its route that would fit on a bus headsign- you can't do it. The route primarily serves Lincoln, Victoria and 3rd/Blaine, but that's far too much for a simple route description, and even that doesn't quite cover all the little twists and turns built into the route to pick up this destination or that transfer point. And the 10 is simple compared to the planning nightmare that is the 13, which can't even figure out which north-south arterial it wants to use. (It uses Central, Arlington, and Colorado before winding its way around Crest, back to Arlington and down Tyler.)
Compare these routings to San Francisco Muni's policy of associating a route with a given street, and naming the route accordingly (N-Judah, 14-Mission, F-Market & Wharves, etc.). Every stop, headsign and route map there displays the name of the route, making it relatively simple to determine the principal service area of that route with nothing more than a glance. If you want to head up Mission, it's as simple as grabbing the bus that says "Mission". Muni is a legible system. RTA is not.
RTA has proposed doing a lot of service upgrades, schedule re-structuring and re-routing in order to get the system ready for the Magnolia Avenue Rapid line (which is still a few years off). One thing they want to do is get a core group of routes under 40 minute headways, and schedule them in such a way that they make timed connections to the aforementioned Rapid line when it shows up. This is an admirable goal, to be sure, but if significant improvements in the legibility of the system aren't made, new riders will be put off of the system simply because they don't know where the buses go. (I've seen this in action before- some UCR students heading up Canyon Crest from campus will actually refuse to ride the "white bus", the 16, and will allow it to pass them up in order to wait for the 51 Crest Cruiser "trolley" even though the 16 would work just as well.) This probably starts with streamlining routes, and then coming up with a system to simply indicate where each route runs.