The melting point of a compound is a reproducible, easily measured property of a solid.  So a melting point determination is a convenient way to confirm the identity of a compound.  Furthermore, because impurities both lower the melting point and broaden the melting point range, taking the melting point of a compound can tell you about the compound's purity.  A sample with a broad melting point, if done correctly, would be impure.  A sharp melting sample is pure (unless it is a eutectic mixture - optional discussion here).

Melting point and freezing point are essentially two aspects of the same phenomenon.  Cool a liquid, it will freeze to a solid; heat a solid, it will melt into a liquid.  The temperature at which these two processes occur should be the same (except if there is supercooling, which we won't need to go into.)
If you think back to General Chemistry lab, probably second semester (on this campus it's CHM 112) you'll recall a lab called "Freezing Point Depression" aka F.P. Lowering.  If a solute is added to a solvent, the solvent's freezing point is lowered.  Typically in these labs you melt (there's that word again) a pure solid, or a mixture of two solids, and then let them cool and watch them freeze.  If the pure solid freezes at 80 degrees, then the mixture will freeze at, say, 76 degrees.
In CHM 112, a pure solvent has a higher freezing point than a solvent mixed with a solute.  Rephrase & update:
In CHM 245, a pure solid    has a higher melting  point than a solid    mixed with an impurity.

If the sample you are using is made of large crystals, use a mortar and pestle to grind it into a fine powder.  place the sample on a watch glass, and put a small amount of your compound into a melting point capillary.  These 4 items are shown here.  You can pack the crystals in the capillary by tapping it on the benchtop, or by dropping it through the long tube as described in the "Lab Manual".  The crystals should occupy no more than about two millimeters of the capillary.

Here is a picture of the simplest type of melting point apparatus we use, the "Meltemp".

The "Electrothermal" is the other melting point machine we use in Organic Lab I.  We have two illustrations of this one, a wide shot and a close-up. You can even look into the melting point apparatus to see the compounds melt.  As you can see from the illustration, the tube contents on the left are beginning to melt, the middle one is already melted, and the right one is still solid (also there's a little too much in the tube on the right).

In the first part of the lab, you will calibrate the melting point apparatus.  The "Lab Manual" describes how to take the melting point of a substance that has an unkown melting point.  FOR THIS LAB, you know the approximate melting points of all your samples.  You do not have to do a fast preliminary determination.
For the calibration, carefully take the melting point of three solids.  You won't need to label the little tubes, because you'll know their contents' melting points.  Please remember that each apparatus has three slots to accomodate capillaries - so the melting points can be done side by side by side sequentially.  The rate of heating should be ~ 1 or 2 degrees per minute near the melting point.  Between melting points please heat faster - otherwise the determination of something with a 145^o melting point will take one to two hours!!
Be sure to record the m.p.'s as a range.  Compare the highest number in the observed m.p. range to the literature values (make sure you've looked these up and written them into your bound lab notebook before class.)  Apply any corrections to subsequent measurements.  In future labs, to calibrate the instrument, you will measure the m.p. of a known whenever you determine the melting point of a solid.

In the second part of the lab you will be given an unknown.  It will be one of three compounds which do not differ by much in melting point (all around 130 - 133).  The idea here is to take mixed melting points:  mix each of the possible compounds with your unknown (a 20/80 unknown to known ratio is a good place to start).
If the resulting m.p. is sharp and up near the expected temperature, then the unknown is identical to the compound you mixed it with.  If the unknown is different from the other compound, it (the unknown) will act as an impurity - a broad range and a low melting point are expected.
Again you have only three samples to run.  (You don't really need to do the melting point of the unknown by itself).  Again please use the three slots in the melting point apparatus.  As you heat the tubes, watch for melting.  After two samples melt ... you're finished.  Think about it.