Its the fruiting bodies (toadstools or mushrooms) of a fungus living in the soil, which has mycelium year round under the ground - these will pass on their own shortly, but will likely be back next year. You can break them off if you don't like looking at them, but you can't kill the mycelium nor remove them. Is there any dead wood in the vicinity, like a tree stump or something? If there is, have that removed/ground out to 18 inches down. It could actually be honey fungus, which might be a concern because that affects living wood too...

I enlarged your photos to get a closer look and it appears to be eminating from the trunk of a tree. If the trunk is one from a live tree there could be trouble brewing as Bambo said in B's very informative answer.

As advised, try and dig down to recover any dead woody material and then I would try and kill the fungus with a treatment of Armillatox. My understanding is that it was recommended as a treatment for honey fungus but due to the up-to-date regulations regarding garden chemicals, it can no longer be advertised for its control. Have a look at Armillatox website. Your local garden centre would be breaking the law if they advised you to use it.

It doesn't work anyway, Jimmy - RHS trials years ago confirmed that. The only thing that might work, if the mycelium are not that advanced, is to remove 6/10 square feet of soil, going down 6 feet minimum, getting rid of it and then buying in new soil. But no guaranteed results... by the time people notice the toadstools, its already too late, usually, its widespread under the ground. There are honey fungus resistant plants though, depending on how virulent the particular honey fungus is.