Conocybe filaris, like all fungi, have a very unique and interesting lifecycle. The life cycle of fungi differs from other organisms because of the domination of the dikaryon stage. The dikaryon stage is a portion of an organism’s life cycle where cells from two different parent organisms fuse, but their nuclei do not. This dikaryotic stage differs in dominance throughout all of the different phyla of fungi, but in Basidomycota, the phyla where Conocybe filaris is found, the dikaryotic portion of the life cycle is dominant.

Basidomycetes reproduce in two different ways. The first, happening less frequently is asexual reproduction. Asexual reproduction occurs through budding, and by the formation of asexual spores. These asexual spores are produced by mitosis alone, and grow to form primary mycelium.

They can also reproduce sexually, through the formation of Basidiospores. This process is a bit more complicated than the formation of asexual spores, and is the preferred method of reproduction for Basidiomycetes. For sexual reproduction to occur, hyphal tips from two different primary mycelia must make physical contact with each other. This fusion is called a mating event and results in the formation of a secondary mycelium that is in a dikaryotic state.  Under the right conditions, these secondary mycelia will produce fruiting bodies in the form of mushrooms. These mushrooms are dikaryotic.  

The process of forming the Basidiospores takes place in the gills of a mushroom. Gills are important not only because this is where the Basidiospores are formed but because of the surface area that they provide. The formation of Basidiospores takes place on club like structures called basidia. The cells in the basidia are dikaryotic and contain two nuclei. These nuclei fuse in the basidia in a process called karyogamy making diploid cells which immediately undergo meiosis resulting in haploid Basidiospores.   

These Basidiospores are then released from the gills of a mushroom into the wind and dispersed to the world to germinate, grow, and repeat the process all over again.  

Below are links to a great graphic taken from TomVolkFungi.net that shows the complete life cycle of a Basidiomycete, and a explanation for that graphic.

Graphic

Explanation of the Graphic

Check out some other organisms that reproduce in the exact same way:

Ganoderma lucidum

Piptoporus betulinus

Psilocybe cubensis