The passive RFID tags have no internal power source and they draw the power from the RF waves sent by the interrogator. They communicate with the interrogator by reflecting and modulating these waves, which results in relatively short read ranges from a few inches to approximately 15 feet. Their memory is limited.
The active tags on the other hand, have their own power source (a battery) and a transmitter and use these two components to broadcast the information to the interrogator (they can broadcast even when the interrogator is not present, this is called beaconing).
This type of tags can communicate over hundreds of feet and have very large memory.
Semi-passive tags are somewhat of a hybrid of these two types of technology. They have a power source but no transmitter and the battery is used to aid the communication. The signal from the reader is still reflected, however, the battery powers the chip, so it does not need as much energy from the reader, which allows responding even to weaker signal and results in longer read ranges than what could be achieved with traditional passive tags. Read range for semi-passive tags could be counted in dozens of feet and they can have also extensive memory.