The 555 uses a bipolar totem-pole output. If you want rail-to-rail output swings, you might try using the CMOS version, the 7555 or mc1455. The CMOS version has a much lower drive capability, though. The output only swings close to the supply rails if you're driving one or two TTL loads.
This link shows the internals of the 555, along with the theory of operation and a fairly detailed description of each pins' operation. (Q20 - Q24 make up the output stage).