EFM...what?

It's pretty important to be comfortable during labor.  Especially as the contractions get stronger...you want to be in a position that is not only comfortable for you but also aides your labor.  Being comfortable in it of itself is an aid in labor progression.  Having the option to get up and walk around is also a great thing.  What isn't helpful is to be forced into a position and unable to move or walk around at will.  Many hospitals will hook you up to a continuous external electronic fetal monitor (EFM) as you come into labor and deliver.  It's 2 straps wrapped around your belly: one tracking babies heart and the other tracking your contractions (a tocodynamometer).  It then prints out a sheet of paper so nurses and doctors can keep track of your 'progress.'  Needless to say, these straps are connected to wires which are connected to the computer, meaning...lack of movement.  Once connected, you are pretty much forced to lay in the bed.  Hopefully you can still at least move from one side to the other and not have to stay on your back.  If your lucky, maybe you can at least stand next to your bed.
There is also an internal electronic fetal monitoring.  This is even less comfortable.  A thin, spiral wire electrode is placed in the skin of the baby's scalp to detect the heart and a tube (catheter like) is placed with in your uterus to measure contractions.  Internal is more accurate but clearly more evasive than the external.  This monitoring requires breaking your water and the skin of the baby's scalp.  Breaking your water prematurely may cause complications itself and in most hospitals start the clock to push that baby out.
So what is the purpose of this monitoring?  For the nurse or doctor to keep track without having to be near.  They can check from their office or station all the women in labor as once and not have to get up and walk around to each individual room.  Or they can simply enter your room and go to the print out and not have to bother you.  However, that might make you feel unimportant in the process since they aren't really paying attention to you.  Trust me, you know when you're having a contraction and how the intensity is progressing.  You don't need a monitor to tell you that.  You're partner may also start to focus on the machine instead of listening and waiting for you.  This monitoring is also helpful to hear the babies heart.  This is a good thing!  The issue is that reading the results is very complex and even experts disagree what different heart rate patterns mean and when intervention is truly neccesary.  Fetal distress is a shortage of oxygen, not simply a change in heart pattern but if there is a change your doctor may very likely jump to the conclusion that the baby is in distress and call for a c-section only to pull out a perfectly healthy baby that had no problems.  This is becoming more of a problem because doctors infrequently truly know what a natural, normal labor and delivery look like and what the heart patterns mean.  Since they are taught how to handle and deal with a crisis, they might jump to an intervention because that's all they know without truly understanding what is going on. 
As I said, hearing the babies heart is a good thing and something that does need to be monitored.  There are ways other than continuous monitoring.  Ask to be intermittently monitored.  Instead of being constantly hooked up, you'll only be hooked up about 10-15 min every hour.  So the greater part of the hour you can be moving around or lay in whatever position you find comfortable.   See if they have a portable radio-transmission (telemetry) unit.  There are 2 types.  One is where you wear a radio transmitter around your neck and those wires are connected to the belt.  The other (and newer version) is wireless.  These are waterproof and gives you a broader area to move/walk about.    If you must be continuously monitored see if they have one of these...it's the best option for you to be comfortable and allow labor to progress.
The least evasive is a fetal stethoscope.  This requires a nurse or doctor to be with you frequently  and studies have shown this method allows the birth of healthy babies with fewer c-sections.  Unfortunately since you need to be check often, many hospitals don't staff enough people for this option.  There is also a hand-help waterpoof telemetry unit so you can be in the bath which being monitored. 
Find out what your hospital requires.  Some will force you into one option...be sure it's an option you feel comfortable with.  As always, read up on the issue!