How to identify an unknown compound with spectroscopic data?
Have a look at typical IR bands (other source) and identify them.


   - 3424 phenolic $\ce{OH}$ stretch
 - 1640 aromatic $\ce{C=C}$ bending or $\ce{C=C}$ alkenyl stretch
 - 1264 aromatic $\ce{C-O}$ stretch
 -  747 aromatic $\ce{C-H}$ bending


Have a look at you spectrum, identify your residual solvent signal.


    7.15 is chloroform $\ce{CDCl3}$


Have a look at the typical $\ce{{}^{1}H-NMR}$ shifts table and identify the protons.


   These are aromatic protons


What is the summary of your first conclusions?


   It's an aromatic compound with an hydroxyl group.


How many protons?


   multiple of 5


Calculate the coupling constants via $$J=\Delta\delta_{\mathrm{ppm}}\cdot\nu_0$$ and identify the splitting pattern. (I can only assume it is a 500MHz spectrometer, hence $\nu_0=500~\mathrm{MHz}$.)
Example: Doublet at 7.55 ppm:
$$J=(7.5615-7.5461)\cdot500~\mathrm{MHz}=7.7~\mathrm{Hz}$$
Solutions:  


   7.55 doublet, $2\ce{H}$, $J=7.7~\mathrm{Hz}$
 7.40 doublet of doublet (fake triplet), $2\ce{H}$, $J=7.6~\mathrm{Hz}$, $J=7.5~\mathrm{Hz}$
 The last one is tricky because there is one peak not picked
 It should be at 7.30 a doublet of doublet, $1\ce{H}$,  ${}^3J=7.7~\mathrm{Hz}$, $J=7.6~\mathrm{Hz}$  


Disclaimer:
Please read long's answer and follow his thoughts. They make a lot of sense and hint that the compound we are looking at is not the one I am proposing. But due to my lack of current knowledge, I cannot make another suggestion.

Combine all you see and you will get a clue which substance it is.


   7.55 ortho
 7.40 meta
 7.30 para
 Phenol.