Wi-Fi association
Association is the handshake by which a wireless device officially joins a Wi-Fi network through an access point. It is like checking in at a hotel front desk: you find the right hotel by its sign (the SSID), confirm you are allowed in (credentials), and only then does the desk register you as a guest and start handling your mail. Until you have associated, the access point will not carry your traffic.
Step by step: the device first discovers nearby networks, either by listening for the access point's beacon frames or by actively probing for an SSID. It then authenticates (in modern Wi-Fi, proving it knows the WPA2/WPA3 credentials), and then sends an association request; the AP replies with an association response and an identifier, and from that moment the device is a member of the AP's basic service set and may send and receive data frames. Association is purely a link-layer relationship — it is about being allowed onto the radio network. Getting an IP address comes afterward, usually via DHCP, and is a separate step.
Why it matters: association is the precise moment connecting actually means something on Wi-Fi, and understanding it untangles common confusions. You can be associated and still have no Internet, because association only gets you onto the local network — addressing and the upstream link are separate. When you walk across a building, your device re-associates from one access point to another (a handoff) while keeping the same SSID. And a device can be associated to only one access point at a time, which is why your phone briefly drops as it switches APs.
Your laptop says Connected, no Internet. That is association without addressing: it successfully joined the access point's basic service set, but DHCP did not hand it a working IP address, so traffic can reach the AP and go no farther.
Associated joins the radio network; DHCP gives you an address.
Association is not authentication of the network to you — it proves you are allowed on, but a rogue access point can also accept your association. Trusting the far end still relies on higher-layer security like TLS.