It is exactly a handoff (that's actually the technical term). Most APs will do it automatically because it actually doesn't rely on the AP so much as the client.
When the client finds another AP that it can access with a stronger signal, it will automatically send a disassociate/re-associate packet, and then bam, done. Now, let's say you are downloading your file, and you were just handed off to a different AP. Unless full mesh networking is set up, there will be a time, usually in milliseconds, seconds if the APs are overly burdened, that your download is paused. If those milliseconds are unacceptable, there are other options in mesh networking. (If you want to know more how the ap's know to continue your download, I think that's more an inbox question for wendell, I don't think I can explain it well)
To set up full wireless mesh networking, dd-wrt allows for OLSR, which allows allows your network equipment to talk to each other. The APs will then calculate the best routes for clients to take, and it will handoff clients accordingly. However, it assumes that you have 100% network reliability AND it assumes that there are additional routers in between subnets, and the way the dd-wrt wiki has you do it it assumes each AP is in router mode.
This is where WDS-Mesh comes in. WDS-mesh is similar to OLSR in that it communicates with other ap's for the best route for their clients, but is different in that by default it will act more like a wireless bridge, no need for a lan cable in between the two.
It's a good option if there's no way to send a lan cable out there, but I was out for speed when I set mine up, so I put in some scripts to fail over to WDS if the powerline goes down. My set up is a bit strange, I have 3 wireless networks, one main at 2.4/5, let's call it "bob-net," one guest at 2.4/5 "bob-net-guest," one hidden wds at 5 "bob-net-wds." During normal operation, wireless vlans keep the wds, main, and guest separate, that way I don't get a broadcast storm between the wds and lan segments, but if a powerline goes out, then wds automatically switches its vlan to link in with the main and guest, and switches its vlan link with the powerline network off. Then, every 30 minutes thereafter it will switch the vlans back to default operation. (hopefully that made sense I think wendell could explain this better lol)
If you are fine with a few millisecond pause between hops then something like a wds or olsr is not necessary, you can just set up your second router in AP mode like I said in the previous post and go, then handoffs will happen on their own.