An observable pattern in the data.
In general, a trend is an observable pattern in the data. Often this concept is used in time-series analysis but not only. For instance, in a scatter plot the line which most closely fits the data points is also referred to as trend. It may be linear if the trend line is fit with linear regression for example, or non-linear if a polynomial smoother is used.
In the widely used context of time series, a trend is the underlying long term direction of the data. It can be exploited to make predictions about future values of a given series. For instance, moving averages (MA) models make use of this feature of the data. Sometimes it is easy to detect trends via eye-balling, i.e. visual inspection, though in many real-life instances this requires more sophisticated methods. An example is high-frequency price data.