A deep space probe was a long-range unmanned space probe used to study phenomenon in deep space, far beyond the range of manned exploration.
Earth deep space probes of the 21st century included the Nomad probe launched in 2002 and the first warp probe Friendship 1 launched in 2067. Both were sent into deep space to seek out alien life. (TOS: "The Changeling"; VOY: "Friendship One")
In the alternate reality, Starfleet used the Magellan probes to chart the Necro Cloud. One of these probes was captured by Krall in 2263 and used to link up with the computers aboard the Enterprise and Starbase Yorktown.(Star Trek Beyond)
The deep space probes used by Starfleet and the Federation in the 24th century had radioactive material in their casing. The radiation was strong enough to interfere with normal comm badge signals and cause radiation poisoning. The Romulan Star Empire was known to monitor the telemetry sent by the Starfleet deep space probes. (TNG: "Tin Man", "Thine Own Self")
The Vega 9 probe was a deep space probe launched by Starfleet to study the Beta Stromgren star, as it entered the final stages of an alternating cycle of expansion and collapse that would result in a supernova explosion. Beta Stromger was at the time 23 parsecs beyond the furthest manned exploration to that region. The probe reached the system in 2366 and discovered the "Tin Man" orbiting Stromgren. (TNG: "Tin Man")
In 2370, a deep space probe went off course and crashed on Barkon IV over a hundred kilometers from the nearest settlement. Lt. Commander Data was sent from the USS Enterprise-D to retrieve the wreckage as he was immune to the radiation. Data collected the radioactive fragments of the probe casing, but as he was attempting to download the sensor logs from the on-board computer of the probe, he suffered a power surge, that overloaded his positronic matrix resulting in amnesia. (TNG: "Thine Own Self")