and you don't have to start at grade 1 and progress through every grade. You can jump in wherever suits you best and miss the odd one out if you wish. Or if you like to collect the whole set, you can take each one. There are usually 2 or 3 times per year when you can take an exam - say December, March and June.They're a measure of progress. Usually a student will prepare with the music teacher, who'd assess a suitable level to attempt. No point in trying for grade 8 when you're playing at grade 1 for instance. All the details are on the web sites. And it's possible to sit the ABRSM (not sure about Trinity) internationally.
We have different exams in Germany, and they're mostly voluntary, although to get into university for music, you need an exam assessed standard that is, as far as I know, equivalent to grade 8.
That is if we exclude the third examining board - London College of Music - validated by Thames Valley University (TVU). The last board is the only board that offers Jazz Grades for Brass Instruments (trumpet and trombone) above Grade 5.The there are 2 main examining boards Guildhall and the ABRSM.