Decomposing a series into its parts
Most real-world time series can be usefully thought of as a combination of three components. Trend is the long-run direction, a slow rise or fall that persists well beyond any single cycle, like steadily growing user signups. Seasonality is a pattern that repeats at a fixed, known interval, like retail sales spiking every December or website traffic dipping every weekend. Noise, sometimes called the residual, is whatever's left over after you account for trend and seasonality, the irreducible randomness that no model can predict away. Decomposing a series into these three pieces, either visually or with a formal decomposition method, is usually the first diagnostic step in any forecasting project, because it tells you what structure is actually there to model.
These components can combine additively (the series is roughly trend plus seasonality plus noise, when seasonal swings stay a constant size) or multiplicatively (the series is roughly trend times seasonality times noise, when seasonal swings grow as the trend grows, like holiday sales spikes that get proportionally larger as a business grows). Picking the wrong combination mode leads to a decomposition that doesn't actually isolate the patterns you're looking for, so it's worth checking whether the amplitude of seasonal swings looks constant or scales with the trend before choosing.