The 1 to 8 Grade scale is the core of the UK's music examination system. Its origins date back to 1877, when Trinity College London first started issuing certificates to external students using this gauge. Nowadays there are multiple examination boards, but all their exams share the same core content and are calibrated to the same Grade scale.
In brief, Grade 1 is the entry-level exam and Grade 8 is the hardest. In practice, the number of skills and abilities required to pass each successive tier increases, as well as the difficulty. Grade 1 is simply centred around the performance of prepared basic pieces and scales; while by Grade 8 a student must demonstrate a suite of skills including improvisation, sight reading and a thorough understanding of musical theory (demonstrated in a separate but parallel Theory exam).
Grades 1 to 5 act as a scale of a student's formative musical development: while they will receive certificates in each one, they do not count towards higher education requirements. Grade 5 acts as a gateway exam for Grades 6, 7 and 8, and introduces a theoretical element; a student cannot skip straight to Grade 6, regardless of skill they already have. However, it is possible to start your examined musical career at Grade 5, skipping out Grades 1-4 entirely, if your initial skill level is high enough.
From then on, you will be required to take Grades 6, 7 and 8 in sequence, along with their parallel Theory exams. Each one counts towards a certain number of UCAS points when applying to higher education establishments, although music colleges usually require a student to have completed Grade 8 before acceptance.
For a thorough breakdown of the components of each Grade, see this pdf document courtesy of the Associated Board of the Royal Schools of Music.
Before embarking on their journey up the Grade ladder, neophyte musicians can take a Prep Test, an informal exam with structured content that acts as a 'pre-Grade 1' primer. Equally, once students have passed Grade 8, there is nothing stopping them from tackling the higher education Diploma exams.
It is worth noting that while it is perfectly possible to take Grade exams in more contemporary instruments such as guitar, doing so isn't as popular as for classical instruments. This is probably because the end goal is different: for students of classical instruments aims may be academic, while guitar players who wish to form bands don't necessarily need theoretical knowledge to achieve their dreams.