I have applied to 2 apprenticeships in the past one of which I accepted and one of which I turned down.
The two days varied differently in terms of how well they were run but consisted of the same types of things.
To start with there was an icebreaking session where all of the applicants on that day met each other and did those silly little icebreaking activites.
Next we moved onto some group tasks, the outcome of the tasks weren't really monitored just how each individual worked as part of a team (who put in the most input) (Who had good ideas) (Who took charge) etc...
Then the next steps for my specific assessment days were to have an interview with the hiring manager which at one of them lasted 30 minutes and the other it lasted around 45 minutes.
After this there was an assessment activity related to the role which took around 1 hour.
Then we were free to leave.
Assessment days tend to be quite informal and are a great way for an employer to see how you interact with others, work as part of a team etc...
A good bit of advice is to stay off your phone and try and interact with as many people there as possible throughout the day.
Remember everyone there is Human to and everyone wants you to succeed so don't be nervous and think of it as an exciting opportunity to learn and develop.