What does "24 hour check in" mean?

24-hour check-in means their front desk counter with 24 hours check-in service. No matter what time you check-in they have staff there to service you.

When you make reservation you better give them your flight number and arrival date and time. If you want to have a sleep upon your arrival (28 May) then you have to make your booking a day earlier (27 May) but one night of room charges has to pay. You may consider guarantee your booking by credit card in advance. If booking not guarantee and you have not inform them your arrival time, room may release after 18:00 (their time) if guest not show up. If the hostel full then you have to wait next morning when someone check out.

24 hours check in means that you can check in whenever you arrive the hostel. No matter you arrive at 3am or 9pm, there will be a staff helping you to check in and get place to sleep. Some of European hostel only allows check in in day time.
of cos i will be better that if you can let the hostel know when you will arrive 1 or 2 days before, it will help them to have a better arrangement.