Data coding in social sciences is the process of taking observations (from a a study of some sort) and breaking them down into categories that can be numbered. This is necessary so that the data that you have gathered can be analyzed and correlated with other variables.
For example, if you are doing a study and you want to find out what kinds of factors impact people's attitudes about public schools, you might gather basic demographic data about the respondents. Then you might ask them something like "What do you like about your public school system" or "What do you not like about your public school system." What you will then need to do is to code their responses. You will have to figure out what basic types of responses there are or are likely to be. You will give those responses numerical values. You will then go through all your responses and code your data by assigning each respondents answer to a certain numerical value. For example, 1 could stand for "teachers don't care" while 2 could stand for "school isn't hard enough" and 3 could stand for "school isn't safe." You would go through the responses and decide which category best fits each response.
The process of doing that is data coding.