Physical state of the carbon denoted with "gr"
The letters in brackets indicate state of aggregation (includes state of matter, crystal structure (solids) and atomicity (gases)), therefore $\ce{C_{(gr)}}$ most likely refers to graphite. Often one can also see $\ce{C(s, gr)}$ or $\ce{C(s, graphite)}$ There is a nice demonstration in [1, p. 248]:


  $$\ce{C(gr) + O2(g) &lt;=&gt; CO2(g)}$$
  Here $\ce{(g)}$ indicates that the compound is gas, [...], and $\ce{(gr)}$ that carbon is graphite (not many people will burn diamonds, even if they are chemists). 


P. S. According to IUPAC recommendations, subscript notation is deprecated. 


Metiu, H. Physical Chemistry: Thermodynamics; Garland Science, 2006. ISBN 978-1-315-31491-4.