the result is same for both but the process is different .
for example : ödevimi yaptım. (i did my homework)
ödevimi yaptırdım . (your homework has been done by someone else . you do not have a homework anymore because someone else did it for you .)
another ex.
hergün yemek yapabilirim . (i can cook every day.)
hergün yemek yaptırabilirim. (i can obtain food every day but i am not a cooker lets say my wife is the cooker . )
another one: ev yapmak : building a house (you are the worker)
ev yaptırmak : building a house (you give the money someone else and they build a house for you)
its really hard to explain because i dont think English has a form or word which covers it.
i hope it helps.