A technician license grants you privileges to transmit on VHF and UHF frequencies, which commonly accessed and used by handheld radio transceivers. You can communicate within a few miles with other HAMS, and further boost your signal by using a nearby Repeater (there probably is one near you)

A General license opens up access to the HF bands, which are allow you to transmit and recieve potentially up to thousands (or tens of thousands) of miles using an HF transceiver. An Extra license further opens up more HF frequencies to transmit on.