I've searched for this answer on the web and found little to no information so I'm going to tell you what was told to me when I was introduced. The validity of the answer may
…be in question as this is just how it was explained to me so take it with a grain of salt, my source was my Platoon Sergeant in the Oklahoma Army National Guard. I was told that in the old days a muster stick was used on the battlefield to muster the troops. The leader or commander (or their directed person) would walk out with a long branch that had a flag on it and lift it into the air and wave it around. This would signal their troops to rally on them. If it was during battle it was a signal to help the commander at that location or to regroup after a battle. I'm guessing this evolved into the guidon concept which is still used today but I was told it was originally called a muster stick. I've been unable to find proof of this so I can't call it a fact. I can tell you what it means for me as a national guardsman. A muster stick is something you make during your first annual training (AT) event after graduating from Basic/AIT as kind of an initiation. During AT you typically find yourself in the woods doing Army training so access to trees is easy. You're directed to find a suitable tree branch that can be made into a walking stick. The new soldier must keep their muster stick with them at all times during AT and their mission is to turn it into a very smooth walking stick. This helps other soldiers identify that the soldier is new which could prevent the new soldier from being chewed out for doing something wrong because they weren't aware of a certain rule. It could also attract unwanted attention to the new soldier which could result in the soldier being dropped ("DO PUSH UPS!") by a higher ranking soldier. This is part of the fun, some of you may not understand but others get it. When the soldier feels the muster stick meets "muster" they can present it to their platoon sergeant for inspection. If the stick does not pass inspection the new soldier is smoked (repetitive push ups or situps or other activities until the soldier reaches muscle failure). Heaven forbid if your platoon sergeant gets a splinter while inspecting your muster stick, extreme muscle failure will occur. Once the stick passes muster your next mission is to get signatures from x amount of people during AT. For me it was 45 because I'm with the 45th Infantry Brigade. You must get the battalion commander's and the battalion sergeant major's signature plus 43 other names. Extra respect is gained if you get a signature from the Brigade Commander or his staff. This activity helps introduce the soldier to his/her chain and teaches the soldier about the unit. Typically to receive a signature the soldier must do something to earn it, soldiers get very creative when it comes to selling their signature. Common costs include push ups, singing silly songs, reciting general orders and naming the soldiers in their chain of command. This builds strength and helps integrate the soldier into the unit. At the end of Annual Training all soldiers that are attending their first AT present their finished Muster Stick to their Company Commander for inspection in front of the company formation. The commander will say a few words of welcome and release the soldier back to his squad. One rule about the muster stick is that if someone other than you aquires it because you didn't keep it with you, they take it to the 1SG. If the 1SG gets it he calls your platoon sergeant in, chews on him about not instilling into you the proper level of respect for the muster stick and then the platoon sergeant smokes you. You don't want to lose it. Some soldiers will carve things into their muster stick or shape one end into a phallic symbol, I did not but it is common. Boys will be boys. I made my muster stick in the summer of 1994 and still have it to this day. It means a lot to me and I continue the ritual with any new soldier I get into my unit. They tend to think it is weird at first but by the end of the two weeks they're as attached to their muster stick as I am to mine. (MORE) 
