The main differencea are as such:
Freeview - set of free to air channels available through a standard television aerial (assuming you can pick up these broadcasts in your area and have a suitable ariel installed). Main advantage is the simplicity of installing (since you likely already have the necessary equipment). Main disadvantage is there is limited scope for HD channels - there are currently four and this is unlikely to increase any time soon.
Freesat - set of free to air channels available through a satellite dish. Main advantage is these broadcasts can be picked up pretty much anywhere in the UK and there is increased bandwidth available for further channels, including HD channels in the future (there is no guarantee that these will actually come though!). Main disadvantage is you need a satellite dish installed if you don't have one already.
YouView - this is essentially Freeview, but with the added benefit that the catchup services of BBC, ITV, Channel 4 and Channel 5 are included and accessible in an easy manner e.g. rather than having to go into a separate app, then search for the programme you want, you can simply scroll the TV guide back to when the TV programme was on, then select it and it will play (assuming it's available on these catchup services). Also, all YouView boxes include recording facilities, whereas these are optional on the Freeview and Freesat boxes. Not really a disadvantage as such, but note that you need to have broadband of a minimum 3 Mbps to get reliable access to the catchup services, and a sufficient monthly data allowance to stream any programmes you want to watch this way - if you don't, you might as well just get a Freeview box.
There's lots more to it than that, but this is a high level overview which hopefully is of some help.