A freehold property is one that you can buy outright: you own the building as well as the land it sits on. With this form of ownership, you have control over making improvements to the property (make sure to check with your local council though!), and the only costs you will need to pay typically are related to the mortgage or maintenance of the property. This is the least complicated of the two main ownership types.
Leaseholds are more complicated than freeholds. Instead of owning outright, you will lease out ownership of the property over a set term, which could range anywhere from 99-999 years. These lease terms are very important. While leases can be extended, the closer to the end of the term, the more costly the extension will be. If you were to buy a home for which the term is less than 80 years, it could affect the value of that property over time making it more difficult to extend or remortgage.
Another key difference is various charges you could incur. Leaseholders can expect to pay thousands in ground rent and service charges in addition to the mortgage they have to pay! It is also worth noting that these costs could increase substantially over time, which could also make it more difficult for you to remortgage in the future.