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.

basically yapmak is a verb meaning do or make. yaptirmak is a causitive form of this verb like have/ get/ make someone to do something.

yapmak => i did my homework / im doing my homework yaptırmak => he did my homework for me / he is doing my homework for me ( but i forced him )