It's very, very simple, Bar. If a property is Freehold, it means you own it outright, lock, stock and barrel - the outside, the inside, and any garden, land, or outbuildings included. You can knock down walls, doors, add on extensions or conservatories, paint in bright pink (provided you get Planning Permission for extensions of 'a permanent nature' and there are no municipal byelaws against coloured paint - there will be if it's a Listed Building, for example).
If the property is Leasehold, it means that although you buy the property, you're buying it from someone or a company which owns the Freehold, and they're essentially leasing you the property for so many years. Your solicitor will need to be sure that the Freeholder has not placed any restrictions upon the property (such as no pets, no add-ons, no internal changes, no changes in use without written permission, etc.). A Leasehold USUALLY runs for 99 years from the time you take the property on, after which, it reverts to full ownership by the Freeholder. That's the big difference.
Here's an example: the block of flats I bought my flat on a Leasehold basis is owned by a housing association. They own the Freehold to the property. The Lease dates from the year the flats were built - 1986. It's a 99 year Leasehold, but, unfortunately, that's 99 years less the 19 years from 1986, giving me only 80 years on the remainder of the Lease. At the end of 80 years, the property reverts to the ownership of the association. The not-so-great news is that, suppose I live for 20 more years (gulp!), then die and leave the flat to a relative. As I currently have 80 years Lease unexpired, minus the 20 I live, that will leave only 60 years on the Lease. So, as the property has less and less time left on the Lease, it becomes less desirable to buy since someone entering by the time it's only got 20 years left on the Lease is bound to ask "wtf am I going to do at age 83 when the Lease expires?" So look to properties with lengthy unexpired leases, since unless there's the chance to buy out the Freeholder, future purchasers are usually put off short-lease properties.
With Leasehold properties, the usual deal (check this with the estate agent) is that the Freeholder is responsible for all of the outside maintenance of the property - usually replacing windows, roofing, chimneys that might fall off, repainting or repointing bricks, fixing or replacing drains and drainage, etc. They're usually also responsible for any 'common ways' inside, such as shared hallways and stairs, any elevators, and depending on the property, possibly the yard or garden, car park or garages. All these responsibilities will be noted in your Agreement with the Freeholder. Additionally, you pay the Freeholder an annual charge to cover such costs. The Freeholder should make an Annual Report available to Leaseholders if he/she/it make such an annual charge, showing where expenditures have gone. They may increase these charges every year. Sometimes the charges include some utility costs like water (mine does).
You can sometimes, with the agreement of the Freeholder, buy out the Freehold. Costs vary, but it can be £6,000+ a pop, and that's as long as they agree. That's one way round a building with only a few years left on the Lease. You then become the Freeholder of the whole building.
You also get buildings which have been divided into apartments, advertized 'with share of Freehold'. This means that the individual owners of the flats own their property outright, and generally get together to create a fund to cover the cost of outside building or garden maintenance. Obviously, if the roof falls in, it affects all of the flats eventually, not just the guy in the top flat, so a fund needs to be managed for such contingencies.
Regardless of Leasehold or Freehold, you still pay Council Tax and the usual utilities, minus any that the Freeholder might include in their annual charge, of course.
If I can help you any more, just PM me.