I was looking at michelin pro race tires and there supposed to be a monodirectional casing. What does that mean ?

If you're asking which way they should be put on, you should mount them so that the labels read from the drive-side of the bike. For real style points center the tire labels to the valve stem. Hope thats the answer you're looking for.

If you're asking which way they should be put on, you should mount them so that the labels read from the drive-side of the bike. For real style points center the tire labels to the valve stem. Hope thats the answer you're looking for.
Pro Race have labels and both sides, IIRC, hence the absurdity of the marketing term.

You can probabably pick it up from the other posts, but if you're looking for a definition, "monodirectional" means the tire should be mounted in a specific way, so it rotates in a specific direction.
As the other post said, tradition and custom call for mounting tires so the label faces the drive side of the bike (the one with the chain on it), but with most tires, there's no real reason to do it. High-performance car tires are often direction-specific, and some mountain bike tires are (though it's common to turn MB tires around). The stresses on road tires are low by comparison to cars, and tread design isn't very important in their traction capabilities, so I suspect there's as much marketing as science in the recommendation, but it can't hurt anything to follow it.

Someone correct me if I'm wrong, but I think "monodirectional casing" means that the filaments that make up that Michelin tire casing are all laid in one direction. There are no criss-crossing belts laid at 45 degrees to one another. Michelin claims that this means lower rolling resistance. Well, that might be true or not. So either way, casing or tread, it's more or less marketing. Put them on any which way you please.

By the way, the label-at-the-valve convention isn't just style. It tells you where to check the inside of the tire for embedded glass once you locate the hole in the tube.