Technically, a leasehold is a very, very long fixed-term rental tenancy, with a single up-front payment. The tenancy is freely transferable, so there is a market for leaseholds that resembles the property market for freeholds. (A freehold is where the property is owned outright.)
In practice, leaseholds are mainly used to apportion "ownership" within buildings such as apartment blocks, where simple ownership of the land does not sufficiently capture the complexity of the situation.
Problems arise in a number of areas:
First and foremost, leaseholds resemble property ownership, and so many people naively treat them as such. But the value of a lease decreases as time goes by. When only a few years remain, the value drops very quickly. People who are unprepared for this can get a nasty shock, and feel hard done by.
Secondly, and more subtly, the leasehold creates a complex relationship between the landlord and the tenant - just like any rental agreement. The terms are set out in a contract which is specific to that particular leasehold - so they may vary greatly one from another. There are a myriad ways that they can contain unfair clauses, or unexpected terms.
One recent scam is for landlords to create leases that have a small, annual "service charge" (payable to the landlord) whose cost doubles every few years. After a while, the payments become extortionate!
In this case, the landlord is allowed to charge tenants for the cost of some kinds of works to the building. In the lease, that probably looks like a small item, but a clever landlord can specify the works in such a way that the tenants shoulder most, or all of the cost.