Devitrification vs glass transition temperature
This graph comes from a so-called "differential thermal analysis". It is studying the effects of temperature on glass.


Differential thermal analysis (DTA) is a method that heats two sample pans, one with a sample and one empty as a reference so that the effects of the sample pan can be negated. The heating is performed at a constant heat flow and the temperature of the sample is compared to the reference. Any exo- or endothermic process will add or subtract additional heat to the material and cause a spike in temperature upward or downward.




  I dont understand what the difference between "glass transition" and "devitrification" is, and why one would be endothermic and the other would be exothermic.



Glass transition is the temperature where bonds of a glass can relax and stress can be anneal out of a sample. It is neither endothermic or exothermic but the specific heat capacity increases as the atoms now have additional degrees of freedom.
Devitrification is where enough is put into the bonds that the atoms may rearrange and form crystalline structures from their vitreous state (devitrification). Crystallizing is an exothermic process because the atoms become more ordered and minimally space compared to a vitreous state, this reduces the strain in the bonds, releasing energy.