What is the difference between analogue & digital signal & why a UHF aerial is required to receive Freeview|HD?

Digital signals come in digits (e.g. 1's & 0's - discrete units that have discrete possible values to indicate a number or sequence of numbers).  Each discrete value is defined as a range of signal parameters as encoded by the emitter to be deciphered by the receiver.

Analog signals come in a continuous domain of signal parameters, corresponding to a measured value that is a continuous concept.

The advantage of digital signals is preserved-quality of information, regardless of presence of noise.
The advantage of analog signals is that they are easier to measure and decode, and that they process quicker, and they carry more information should noise be minimal.

With the advancement of digital processing speeds, analog signals no longer have much of a speed advantage over digital. 

The above is attributable to gintable (who seems to be really into physics...)

UHF stands for Ultra High Frequency, this describes the band of frequencies in the Radio Spectrum (it's up there, in the air).

Digital entertainment content, carried over on Freeview|HD, are trasmitted as digital data (after encoding), in the UHF band of frequencies. 

Analogue TV have been transmitted - in the form of analogous waves - in the VHF band (Very High Frequency band). 

VHF band (for analogue) sits below the UHF band (for digital) in the Radio Spectrum, this is one of the reasons WHY a UHF aerial is required to receive DIGITAL content (the old rabbit ears - designed to receive VHF signal data - are not recommended).

Digital signal is also 1's & 0's (discreet units of data), so when the UHF aerial is not aligned correctly with the transmission stream (the rays of data emanating from the transmission tower...for want of a better way to describe it), or when your UHF aerial is blocked by trees, cobwebs, or has just with time - gotten a bit rusty: you lose signal quality (& if you're far away from the site, signal strength). 

Under these less-than-ideal scenarios, you get drips & drabs of the data that collectively make up a part of a show - the digital device then tries to piece together what it can get from the aerial at any given moment in time, rendering something like what Picasso might've done on your TV screen...or something from The Matrix - pixelation & distortion of images & sound...

Some clever people have even designed cool stuff around this concept that we're surrounded by pixels...

What is HD?

High-definition video or HD video refers to any video system of higher resolution than standard-definition (SD) video, and most commonly involves display resolutions of 1280×720 pixels (720p) or 1920×1080 pixels (1080i/1080p).

High-definition image sources include terrestrial broadcast, direct broadcast satellite, digital cable, high definition disc (BD), internet downloads and the latest generation of video game consoles. Most computers are capable of HD or higher resolutions over VGA, DVI, and/or HDMI.

The optical disc standard Blu-ray Disc can provide enough digital storage to store hours of HD video content. DVDs look best on screens that are smaller than 36 inches (91 cm), so they are not always up to the challenge of today's high-definition (HD) sets. Storing and playing HD movies requires a disc that holds more information, like a Blu-ray Disc.

Sony has provided a comparison grid that shows the difference between HD and SD...

What is signal strength?

What is signal quality?

Why do I need to align my UHF aerial / satellite dish?

How could it be my antenna / set up causing reception issues when I've touched nothing? (Just on that...I often see large birds land on aerials & have always wondered whether they create any reception issues for people by doing so....)

How does transmission work? (And what exactly is "transmission" in any case?  What is being transmitted?)

...

Possibilities are endless...