Let's say I've got two devices connected to my Access Point, a laptop and a tablet. If the laptop sends unicast traffic to the tablet, I understand that it must go through the AP. However, how is broadcast traffic from the laptop handled? Does this traffic too go through the AP, or is it sent from the laptop to the tablet directly?
In infrastructure mode (using a WAP) everything runs through the WAP. For example, your two hosts will be in range of the WAP, but may not be in range of each other. Also, one of the devices may be at such a distance from the WAP as to need a lower rate, which is why broadcast and multicast traffic on Wi-Fi is sent at the lowest rate of the WAP.
Does WiFi broadcast traffic from a station go through the access point?
In infrastructure mode, clients typically only send traffic to the AP (ignoring exceptions such as 802.11z capable clients). As such, clients don't typically broadcast traffic, even when the traffic is broadcast. Rather it is unicast to the AP which in turn broadcasts the frame.
However, how is broadcast traffic from the laptop handled? Does this traffic too go through the AP, or is it sent from the laptop to the tablet directly?
Since any single client on a wireless network is not assured to be able to reach every other client, clients send their broadcast traffic to the AP as a unicast (which uses higher data rates, as I will get to in a minute). Since to be connected to the wireless network each client must be able to exchange frames with the AP, only the AP has any level of assurance that traffic it sends can be received by all clients.
So when the AP receives traffic to be broadcast, it performs the role of broadcasting the frame to the network, including both the wired and wireless side of the network. On the wireless side, the AP will use the lowest base/basic/required data rate that all associated clients can support. This helps to ensure that each client will receive the broadcast.
However, some wireless systems can perform a broadcast-to-unicast conversion which makes the AP send a unicast frame to each client instead of a single broadcast frame. There are a couple of reasons that this may be implemented. First, unicast frames are often sent at a much higher data rate, so it may actually take less "airtime" to send multiple fast unicast frames rather than one slow broadcast frame (for example, 10 frames at 200+ Mbps vs one frame at 6 Mbps).
Second, broadcast frames are not acknowledged by the clients, so there is no way to determine if the clients actually received it. With unicast frames, each client will send an ACK for received frames and if the ACK is not received the AP will retransmit the frame.