Decades ago stock trades were sent out electronically to machines which printed each order (price volume etc) on a narrow paper tape. People trading off floor in brokers etc would read the tape as the new orders came in and use that to try and figure out where prices were going.
The last tape machines were taken out in about the 1970s I think and replaced with computers. The modern from of tape reading is to watch the order flow on a screen and see what prices your stock or futures are trading at and what volumes are behind the trades. You will also hear it referred to as Time and Sales information. Some traders say its all they need in order to trade.