Mashiyat means "will power", a person's ability to make choice and use their will power. It is a name for girls derived from a Quranic root, SH-Y-A, mentioned in over 200 places in the Quran, such as Prophet Musa alaihis salam saying in 18:77: "If you had so willed, you could have earned a wage for it.". It can also be spelled as Mashiat, Masheeat, Mashiah, Misheeah, Mashiyah.
Aylin is a Turkish name meaning "halo around the moon." It doesn't have an Islamic meaning, but Muslims can use it since the meaning is good.