What is the purpose of the capacitor and resistor in this op-amp circuit?

It is a Zobel network also known as Boucherot cell, meant to stablize the amplifier when no load (speaker) is attached. It compensates the increasing speaker impedance at higher frequencies and prevents high frequency oscillation.

(1) What Jippies says.

(2) The Boucherot cell (seen here) is a special case of a Zoebel network.
Zoebel networks are a matching network aimed at transforming the impedance of a frequency variable "target" to make the overall result more like a pure resistance with a wider flatter frequency response. For too much detail see Wikipedia - Zoebel network.

For speaker application see section "Zobel networks and loudspeaker drivers".
In the speaker application the component between the centre of the RC and the speakers notional LR is missing (as the speaker's distributed LR has no physical tap - and you can swap R & C so it is no longer a Zobel bridge but still works.

Interest:

Original 1923 paper is : Zobel, O. J., Theory and Design of Uniform and Composite Electric Wave Filters, Bell Systems Technical Journal, Vol. 2 (1923), pp. 1–46.

Image of full 1923 article here:
http://alcatel-lucent.com/bstj/vol02-1923/articles/bstj2-1-1.pdf Link now dead. https://archive.org/details/bstj2-1-1

Munted text version here: http://archive.org/stream/bellsystemtechni02amerrich/bellsystemtechni02amerrich_djvu.txt

Original title is "Theory and Design of Uniform and Composite Electric Wave-filters"

Zoebel is spelt Zobel in the paper.

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1st page of original here

http://onlinelibrary.wiley.com/doi/10.1002/j.1538-7305.1923.tb00001.x/abstract

47 pages of original here -

Online viewable: https://archive.org/details/bstj2-1-1

Downloadable PDF: https://ia801902.us.archive.org/8/items/bstj2-1-1/bstj2-1-1.pdf