Next Letter shows a short stretch of the alphabet, such as L M N, and asks what comes after. It checks whether a child knows the order of the letters, not just the song.
What your child is learning
Most children can sing the alphabet well before they know it. The tune carries them along, and the middle part, "L-M-N-O-P", often comes out as one long blur. Being asked to continue from an arbitrary point shows whether each letter is known as a separate thing with its own place.
Alphabetical order is a practical skill. It is how registers, dictionaries, indexes and contact lists are arranged.
How to help
Sing or say the alphabet from the beginning if needed, and stop at the gap. That is a fine way to start.
Then try beginning a little earlier each time instead of at A. If the letters are R S T, start from P.
Break the alphabet into chunks. Many people learn it as A to G, H to P, Q to V, and W to Z, following the tune. Knowing where each chunk starts makes it easier to jump in.
Have an alphabet strip in view. Seeing the letters in a line while playing is a help, and your child will need it less and less.
Watch the middle. Mistakes cluster between J and R. The wrong choices offered are always near neighbours of the right letter, so a guess will not do.
Taking it further
Put things in alphabetical order by first letter: three toy animals, the family's names, books on a shelf.
Ask what comes before a letter as well as after. It is noticeably harder.
Of the letter HTML5 games on this site, this is the quickest to play, and a good warm-up for the others.