Imagine you are predicting a basketball game. Features would be things like:

Season Win/Loss ration of each team

Number of wins in a row

Proportion of points by best player on team

etc etc.

These are pretty easy, but then sometimes you need to do work to generate the features - this is called feature engineering.

Some features which might need more "feature engineering":

Average sentiment of social network posting by team members

1-on-1 effectiveness of defensive players vs opposition offense (something like this might require video analysis and sometimes manual annotation)

In the computer vision world, things like edges and points are often used as features.

Deep learning is nice because it automatically learns these features given enough time. Otherwise people spend a lot of time building algorithms like SIFT etc.