A vortex manipulator was a form of basic time travel developed by the Time Agency of the 51st century. The accuracy of travel the vortex provides is unclear, Jack Harkness arrived in 1869 when aiming for the late 20th century. A setting on the sonic screwdriver is able to enhance the accuracy of the travel path, as the Doctor is able to use it to guide Jack and Martha back from the future back to when they had last left.
Although it was generally used by the Agency, the Family of Blood stole one to follow the Doctor around the universe. (DW: The Sound of Drums) The Doctor considered it very primitive compared to a TARDIS, describing his TARDIS as a "sports car" to Jack Harkness's "space hopper". The TARDIS controls include a vortex manipulator. (DW: Attack of the Graske)
Jack Harkness had his manipulator housed in a Time Agency wrist strap. (DW: Utopia)
Presumably the vortex manipulator created some sort of shield to protect an Agent from the side effects of an unprotected journey through the vortex. This did not, however, prevent some considerable discomfort for the user, as shown by the Doctor, Jack and Martha's responses upon arriving in London. (DW: The Sound of Drums)