How do the lines differ and what exactly do they show?
The Signal line and the Moving Average Convergence Divergence (MACD) are technical indicators used by capital market and currency traders for making investment decisions. Like all technical indicators, these lines are constructed statistically using historical price and volume data.
The MACD and the Signal line are used together in a popular strategy called MACD Crossover. You can see an explanation of this strategy as well as other strategies here.
The rationale behind using the 12, 26, 9 EMA is explained in other StackExchange thread here
The best way to understand the difference is to compare how each indicator is calculated.
EMA stands for exponential moving average. It is a type of statistical average that puts emphasis on recent values in a time series. You can check how EMAs are calculated here