Wi-Fi was a method of wirelessly connecting electronic devices to each other via the internet, for purposes of communication or entertainment. It could also be used as a method of dispersing energy. It had varying qualities of reception.
By 2013, Wi-Fi was practically omnipresent on Earth - the Eleventh Doctor described humanity as "living in a Wi-Fi soup." The Maitland family could access Wi-Fi in their home, using the password rycbar123. The Great Intelligence used an organisation run by Miss Kizlet to upload peoples' souls through Wi-Fi into the data cloud in order to feed its form; this plan was enacted by disguised robots called Spoonheads. (TV: The Bells of Saint John)
In the underwater base the Drum in 2119, the Twelfth Doctor tuned his sonic sunglasses into the base's Wi-Fi, providing an audio-visual feed to the base's computers to let the base crew get a closer look at the ghosts haunting them. He also used the sunglasses to generate holograms, first of Clara Oswald and later of himself, which were projected using the base's Wi-Fi. (TV: Under the Lake, Before the Flood)
In the 52nd century, the Seventh Transept had decent Wi-Fi, despite being a tomb. Dorium Maldovar was able to use his media chip to access the Wi-Fi after he was decapitated and brought to the Seventh Transept. (TV: The Wedding of River Song)