Hello, it means "buy" in this context. This tense does not exist in English, you can translate it like i would like to buy a fridge

Normally it means that I was going to buy but I didn't, but in this context it is just a manner of speaking, it is not formal language. It's just more kind to say like this

- Buyurun efendim, ne arzu etmiştiniz? - Buzdolabı ve televizyon alacağım. || I'm gonna buy a fridge and a television ,,,,,,,,,,, to talk normally - Buzdolabı ve televizyon alacaktım. || I would (like to) buy a fridge and a television ,,,,,,,,,, to empolite the expression

Actually I am surprised because all the answers are wrong. "Alacaktım" literally means, I was going to buy. It is a combination of future tense and past tense, "Gelecek zamanın hikayesi" in Turkish. As you might already know, "acak,ecek" is future tense verb-makers, and "-tı" is past tense-maker, with a consonant assimilation (normally -dı), "al-acak-tı-m", last letter "m" represents the hidden subject "Ben" meaning "I". I hope it is clear now.

almak: 1to take, "2to buy," 3to receive al + acak (future) >alacak ||bare form of the future tense idi was idim i was was will > would -ecek idi / -acak idi > -ecekti/-acaktı alacaktım I would buy

You must thinking I was want to buy.