What is Armenian Knitting?
Armenian knitting, sometimes called the Armenian lock-stitch technique, or simply the lock-stitch technique is a type of color-stranding similar to Fair Isle. It is similar to Fair Isle knitting in that two strands of yarn are carried along the work at the same time. The finished fabric differs in several ways. First of all, when a fingering weight yarn is knitted on US 3 needles, the technique results in a dense fabric with very little stretch. When knitting with US 5 needles, the fabric has a peek-through quality where the floats show through to the front. Letting the contrasting floats show softens the background, giving the finished garment a heathered look. Wherever the foreground has large blocks of color, it too will be heathered.
Cossack Vest - design by Meg Swanson, project by Karen Kiski
When to Trap Floats
If you've ever worked color-stranded (Norwegian, Fair Isle, etc), then you'll be able to work the Armenian technique. It is exactly the same with a couple of caveats. In Fair Isle knitting the rule of thumb is to trap any float longer than an inch, or so -- for fingering yarn it works out to trapping the yarn carried about once every seven stitches.
In Armenian knitting:
- Floats are trapped every other stitch, or every third stitch along the row or round.
- The first stitch of the row is always worked in the background color.
- Avoid trapping floats on the same stitch in two rows next to each other.
- The construction may be flat or in the round.
When done correctly, the floats on the wrong side (private-facing side) will form more or less diagonal lines - as in this photo

Situations to Consider
1. Intarsia
I've already mentioned large blocks of color. Yes, you can use this technique rather than intarsia to fill blocks of color when only two colors are required. For multiple colors it's probably best to keep to Intarsia. And if your pattern calls for a DK weight, then gauge modifications may be necessary when subbing two strands of fingering weight yarn.
Tip: Armenian knitting could be especially successful when stranding one solid yarn and one highly contrasting hand-painted yarn.
2. Motifs
When designing Fair Isle and Norwegian stitch patterns, attention is given to the number of stitches between motifs, specifically to avoid needing to trap yarn. This often results in a lot of smaller "filler" motifs, between larger ones. There is more freedom in Armenian knitting to space motifs widely apart, or even vertically, since the distance of the yarn carried behind is no longer a consideration.

3. Socks and Mitts
Any time you'd like to add colorwork to socks, hats or mittens, the Armenian technique can be a good choice. Knitting with US 3 needles makes an extra-dense fabric which helps keep fingers and toes warm on those cold winter days. An added benefit is keeping small fingers or toes from catching on loose floats!
In Conclusion
The Armenian technique is an excellent choice for colorwork when the finished garment would benefit from a denser fabric, or to minimize snagging. Items to work in Armenian knitting include hats, mittens, socks, and doggie sweaters. Another reason to use this technique is to allow design elements such as large motifs to be worked without intarsia.
With practice you may find yourself knitting almost as fast as with other stranded colorwork.
Enjoy!