Or income
A Kulak was not someone of a certain income or a certain net worth. A Kulak was simply someone who owned (or held a single tenancy) and worked their own land and did not farm it communaly together with other peasants.
The abolishment of serfdom in 1861 had allowed a large section of Russian peasants to become self-owning, and the trend during the latter half of the 19th century was for these to acquire more land, either by shashing and burning, draining marshland or buying land previously owned by the nobility or the monarchy.
However, agriculture in Russia was very ineffective. A three-field rotation system was in use andm ore than half the plows were still entirely of wood 1914. Farming was almost wholly done in mir (communes). A commune was usually a village of peasants who either as tenants (formerly serfs) of the Romanovs, the nobility or the church or as self-owning peasants worked together and shared both labour and rewards. Since land ownership could be split upon inheritance in Russia, the self-owning peasants could through inheritance own a confusing set of plots spread out through the village's lands and down to 1/128ths of a field - if there were any registers or records of what land was owned by whom at all, communal farming was really the only way to farm.
This system had been reasonably effective during the 17th and 19th centuries, when the ability to mobilise many hands at the same time to sew, harvest, dig ditches, tresh and mill was an advantage. However, as iron tools become more common during the latter half of the 19th century, which meant that one man could do more work, this system became less effective compared to having a set of whole plots around your own farmstead and farm them yourself with your family and in some cases a farm hand or agricultural labourer/seasonal labourer. Communes usually needed to agree on any investments, and were poor and conservative and had a hard time securing agricultural loans for investments, as their shares of plots were not usable as collateral for agricultural loans.
Another factor was the increase in the rural population due to high birthrates, vaccines and advancing hygiene and medical knowledge causing a sharp drop in infant death rates - the large families of the peasants meant that there were a lot of people to feed and lots of hands to do manual labour, in many cases way too many hands, and the communes produced little to no surplus in food for the rest of society.
Prime Minister Pyotr Stolypin instituted reforms 1906, that was confirmed by the Duma (Russian parliament) in 1910 allowed peasants to create singular plots in a specific position out of their part of the commune to be owned and worked by them alone.
Kulaks could invest in their land, use innovation, new tools and benefit from hard work in a way that the communes did not, and those that requested their share of the commune to become Kulaks tended to be those that had the most to gain. Thus many Kulaks became if not wealthty, at least relatively well off compared to their peasant brethren still living and working in communes and often used that wealth to further invest in their farms - horses, iron plows, iron treshing machines, iron harrows, articificial fertiliser and so on, increasing the yield of their land and how much land they could farm without having the help of others.
The Kulaks were winners in the old Czarist order and stood to lose their farms to the new Bolchevik order - the Bolcheviks often simply converted the local commune to a collective farm, including Kulak land, which the Kulaks of course resisted - often violently so. As the Kulaks owned a lot of the machinery and horses of the countryside and often produced a majority of the surplus of the countryside, the violent subjugation of them, and their resistance (including destroying machinery and killing horses rather than turn them over to the Bolcheviks).
By 1915, around 15% of the peasant households could be classified as Kulak households
Sources:
http://web.mit.edu/russia1917/papers/0901-PeasantViewsonLandReforms&Governance.pdf
https://economics.stanford.edu/sites/default/files/markevich_march_4.pdf
Russia's Economic Transitions: From Late Tsarism to the New Millennium by Nicolas Spulber
Follow up question: I've heard it claimed by folks like Niall Ferguson that the persecution of the Kulaks was deeply tied to antisemitism and was nothing less than an anti-Jewish pogrom? Is there any truth to this? If so, was this a centrally directed policy, or locals who turned on their Jewish neighbors when presented an opportunity?