Here's how Herbert Danby translates it: "After the Passover meal they should not disperse to join in revelry." His note reads:
Heb Epikoman [Something (the word Afikomin?) in Greek] Cf. Is 30. The joy of the Passover meal with its solemn symbolism must not denigrate into an ordinary convivial gathering. The traditional interpretation, however, is: "They may not finish with desert."It's been pointed out to me that the order of the Mishna itself militates against the traditional interpretation. By the time we get to 10:8 the meal is over. The end of Maggid is discussed in 10:6, and 10:7 gives instructions for bentching, hallel and for the third and fourth cups. 10:9 can't mean "don't finish the meal with desert" because the end of the meal and, indeed, the end of the Seder itself are discsussed in 10:8. The proper place to mention a desert prohibition would have been prior to the end of the meal described in 10:7.
An additional last word
"However, the Mishnah (Pesachim 10:8) commentary by Philip Blackman (Judaica Press, 1963) and Marcus Jastrow's Dictionary (page 104; Judaica Press, 1996) point in another direction. They both derive AFIKOMAN (originally, EPIKOMIN) from the Greek EPIKWMON (EPI + KWMOS), "aftermeal entertainment," and EPIKWMOI, "things belonging to the aftermeal. -- Solomon Landers"
Full disclosure: Danby was an Anglican priest and a famous philo-Semite. I wouldn't accept his opinon on a matter of halacha, but I do think he's qualified to tell us the historical meaning of the word "afikomin." He has no dog in the fight, after all- though I suspect many of you (or Yus, at least) will disagree. FWIW I very much enjoy his translation of the Mishna. It's exceedingly well written and compact. The whole book fits comfortably in your hand, allowing you to imagine what studying the Oral Law may have been like when Rebbi first compiled it.