Why does my Macbook Air keep disconnecting from my wifi only at home? ?

Missing info: What ISP and router and other networking devices do you have that you're using?

It could just be the service it self. Verizon DSL sucks. It's known to do these kinds of weird things; Disconnect devices for little to no reason (DSL is not even close to a "fast" connection or a reliable connection. It can be effected by wind / poor weather.), although the router is on and says it's connected none of the devices to it can connect to the internet. The router has to be rebooted several times each day. 

Verizon marketing advertises 940mbps and fiber optic technology. It's just advertising. Advertisers use verbage that causes sales. It doesn't mean it's the truth. 

I had FiOS and the real truth of it is that it sucks. I had connection issues multiple times per day. Some were the same thing you're describing; some devices had no problems, others would disconnect randomly. With Verizon FiOS I was only ever getting a maximum download speed of 8mbps, very far from "940" and that's actually extremely slow - definitely not enough for a family of 4 each having 2 or more devices using the connection, it would bog down and quit. And I was getting a maximum average upload speed of 2mbps. That is a horribly slow connection. 

I switched to Xfinity and have been with them for 2 months now. The family has not experienced even one stupid, weird, no-reason disconnect from any of their devices. Each device is getting an average of 240mbps download and a solid 10mpbs upload speed. 

The problem may be the service. Nothing you can do about that other than switch providers and get better service. 

DSL is NOT a fiber connection. It's DSL. DSL stands for Direct Satellite Link. It comes from a satellite. The satellite signal is converted in to a current wires can distribute (fiber optics, but not all wires are fiber - sales sales sales!!) and that is what is connected to our homes. DSL loses quality if clouds in the sky are blocking the signal - worse if there's percipitation like rain or snow or heavy winds blowing the receiver(s) around, it loses quality from being converted to a current wire can distribute, and loses quality again over distance travelled through the wires. 

DSL sucks. It's not reliable and it is definitely not fast. 

Wi-Fi signals are also effected by different things. Wi-Fi is radio waves. The radio waves can be obstructed by structures, interfered with by different materials like aluminum and steel which are in the structure of almost every building. If there's metal or steel or other electrical appliances that have and/or effect radio wave quality like microwaves, televisions, radio scanners (like a fire and police scanner), an AM/FM stereo that's turned on, etc in it's path they are an obstacle the signal is negatively affected by. The wireless signal has to find it's way through those obstacles. 

You don't say how many bars of signal strength you are getting, also whether you are connecting to a 5GHz wifi or 2.4GHz wifi, although 5Ghz is faster 2.4GHz has better coverage so may be worth swapping to that

You may be getting interference from neighbouring wireless signals.

1)Change the broadcast channel on the router to channel to a less congested one than the current. You can download netstumbler or inssider (google them) and they will display the broadcast channels of any neighbouring wifi networks

2)Turn off any baby alarms cordless phones wireless doorbells as these use the same 2.4Ghz frequency. Poor electrical fittings fluorescent lights and microwave ovens also can cause interference

3)Update the firmware of the router.

4)if you are at the limits of the wifi range consider a wifi mesh system or moving closer to the router

5) Poor quality router. This is especially true of ISP supplied routers.

6) It is unlikely to be a problem with the wifi card in the Mac, so messing around with the settings won't help

HTH