HI, I do not understand why AEF is a isoceles triangle

Triangle DEF is an equilateral triangle, so all the sides have the same length, in particular, ED = EF.

ACDE is a square, all sides have the same length, in particular, AE = ED

Since AE = ED and ED = EF, so AE = EF. That's why triangle AEF is an isosceles triangle with AE = EF. Hope this helps.