• 義 [ぎ] – justice; loyalty; honor
• 理 [リ・ことわり] – logic; reason
• チョコ – chocolate (abbr.)

As a compound, 義理 means a social obligation or courtesy, and plays heavily on a socially-trained sense of “honor.”  To get an idea of exactly what “obligation chocolate” is and how it’s used in Japan, let’s take a look at a paragraph from Wikipedia:

義理チョコは、一般には、女性がバレンタインの日に、恋愛感情を伴わない男性に対し、日頃の感謝の気持ちを込めて、またはホワイトデーの返礼を期待して贈るチョコレートのこと。あるいはその儀式全般を含有した日本特有の文化を指す。

Obligation Chocolate is, in general, given by women on Valentine’s Day to men for whom they have no romantic feelings in order to express gratitude.  In addition, it can be given as a return gift to those who gave White Day* gifts and expect something in return.  This ritual is peculiar to Japanese culture.

*(White Day is celebrated a month after Valentine’s Day, and involves men giving women candies, marshmallows, even lingerie.)