Like everybody said, that's your water meter. For far more than you wanted to know about all of that stuff, read on.
The pipe coming through the wall with drywall on it is the connection to the city water main. There are two wires clamped to it. The big black insulated one will go to your circuit breaker panel or fuse box; it's there so the electrical service can use the (metal) pipe under your yard as a ground. The bare copper one goes to another clamp on the other side of the meter; it's there so the plumbing in the house is still grounded, even if the meter is gone, or replaced by one with a plastic body.
The yellow handle is a valve. With the handle in line with the pipe, like it is now, it's open. If you turn the handle so it's 90 degrees to the pipe, it's closed. It's a ball valve, so it only takes one quarter turn to get from fully closed to fully open. If you close this valve, it will turn off all the water to the entire house.
The next thing is the water meter, as has been mentioned. A lot of them will normally make a clicking noise if you have something using water; if it clicks when you think there should be no water running, that means you have a leak. Also, that little red triangle you can see through the clear top of the meter will spin, even when a very small amount of water is flowing - to see it, turn the kitchen sink cold water full on, go look at the meter for a minute, then turn the kitchen sink down to a trickle, and go look at the meter again. If you can catch the triangle moving when you think everything should be shut off - you have a leak. I'm not sure what the red sweep needle does. There *may* also be a set of number wheels visible through the clear top of the meter; that number should resemble the ones on your water bill.
The skinny red and green wires connected to the meter, that go into a cable, are for the remote-reading device on the meter; if you follow that cable far enough, it will go to a plastic box or puck on the outside of the house somewhere. The older ones had a connector in the plastic box - the meter reader had to plug a hand-held device into the connector to get the reading. The newer ones are contactless - the meter reader just holds their hand-held device up against the puck for a couple of seconds to get the reading. (Before these existed, somebody from the water utility had to come into your house to read the meter. Sometimes they'd send you a postcard and ask you to fill in the reading and mail it back. )
The next thing is the clamp for the other end of the bare copper wire that keeps the house plumbing grounded.
The next thing with the yellow handle is another valve. Same as the first valve - the handle the way it is now is open, at 90 degrees to the pipe it will be closed. Closing this valve will *also* turn off all the water to the whole house.
You only technically need one of these valves, and a lot of houses will only have one, usually on the city side of the water meter (the first valve I talked about, in your picture). Having two is only really useful when replacing the water meter - closing the second valve means that the plumber doesn't have to deal with all the water in the house pipes running out when they remove the meter.
The last thing is the cold water pipe running up the wall. It will branch off to the "cold" side of all the sinks and tubs, all the toilets, and all the outdoor hose bibbs. It will also go to the inlet side of the water heater.
Like I said, probably way more than you wanted to know about it.
