Coefficients are numbers in front of variables.
For example, in y=2x, the coefficient is 2.
In the case of chemistry, the coefficient is in front if a chemical symbol and is used to balance a chemical reaction.
Example: O2 + Fe= Fe2O3 (with Fe having a +3 ion)
To balance use the following coefficients:
3O2+4Fe=2Fe2O3
Hope this helps!