"Walking beams" are widely used in automated assembly/inspection systems. By means of a WB, a product may be advanced through the track from station to station - all at once, in sync. Of course, the product itself should not be too fragile and should be of a shape that allows track feeding. Most of automotive and some electronic components fall into this category just right.
Eric's description is right, but this is just one type of a WB. There are versions that, instead of up/down motion, engage the fingers (i.e. metal beams that actually apply force to the product) laterally, "from aside". Another type might have the fingers spring-loaded, so the WB has only back-and-forth motion, pushing the product on the forward stroke and allowing the fingers to deflect safely on the back stroke.
Depending on these considerations as well as on the machine throughput requirements and on the flexibility criteria (how often would one need to change over to a different stroke length, if ever), the following controls options come to my mind:
1. As described by Eric, a combination of two air cylinders - back/forth and up/down. Simple but rather slow. A simple 4-step sequencer in ladder logic plus basic fault detection.
2. If flexibility (frequent changeovers) required, the servo version of the previous (rather for back-and-forth motion, don't see much justification for switching up-and-down move to a servo; it is usually a short stroke anyway). Pretty much the same, although can be a bit faster, the obvious extra work to make the servo work right.
3. For higher speeds, one should be interested in complete synchronization of WB motion with a station cycle, i.e. working "by a timing diagram" (a.k.a. "cyclogram" in some parts of the world). Here both WB motions will be implemented via a set of cams (hey, now it is the mechanical guy's concern, not yours!). An AC motor, possibly with some kind of speed control, will run the camshaft, which, in turn, will drive not only the WB, but all the stations also. A "must" in this case is a master encoder to monitor the WB position so obvious interlocks and fault conditions can be programmed. For example, you may want to have your vision inspection station to fire at 60 deg position and to trigger a fault if the inspection will have not complete by 285 degree. Since homing would only be a nuisance, an absolute Gray code encoder (8 to 10 bit resolution) is quite typical.
4. The most expensive solution - same as above, but everything is servo driven and cammed through software. Certainly may be justified for high flexibility along with high speed. Requires most complicated programming, including coordinated motion control using cam tables, master/follower things, virtual axes and such. This also means some higher-end PLC - a ControlLogix, a CS1 and so on. I personally like Yaskawa MP900 series for that. A CNC controller would probably be an overkill, though
One more thing - with a walking beam, product tracking is reliable and easy. A sensor at the beginning of the track - and a shift register in ladder logic - that's all it takes, really...