That sign is called " Circumflex accent " [inceltme işareti, uzatma işareti].

"^" may stand over the vowels a,i and u.  [in loanwords]

One of it´s function is; [inceltme]

- Standing over the letter "a" which is preceded by g,k or l, the circumflex indicates that a "y" sound to be pronounced between the consonant and the following "a". In the syllable "la"  the "y" sound is fainter than in the syllable "ga" and "ka".

Gâvur ---> Heathen

Kâr ---> Profit

Lâle ---> Tulip

I will add some further information to Tunci´s answer

I am told this sign is no longer used in modern Turkish.

But some dictionaries  still use this symbol, as it helps to differentiate words that are spelt the same, but have different meanings. The words will sound different when spoken.

For example

Kâr ---> Profit, Kar ---> Snow

Hâlâ ---> still, Hala ---> Paternal Aunt

Hâlâ mı? ---> Is it still going on?

Hâkim ---> dominant, Hakim ---> Wise man

this is a really helpful post

another question, in one of the exercises there´s the following example: "onlar zengindir" -> shouldn´t it be " onlar zenginler"?

"yaşındayım" is incorrect.. this error is so common that even masters often commit it and never realize if it is actually a mistake  

It should be yaşımdayım

yaşım (1st sg)

yaşın (2nd sg)

yaşı (3rd sg)

yaşımız (1st pl)

yaşınız (2nd pl)

yaşları (3rd pl)

Examples:

Bu genç yaşımda hasta oldum.

Bu yaşımda bunlar da mı gelecekti başıma? 

Yaşımı sordu, söylemedim. 

Yaşımı öğrenip ne yapacaksın? 

Sence yaşım kaç?

Ben yaşımı başımı almış bir adamım.

etc... 

Really scalpel this is such a shock for me always I have used yasindayim, and always I have seen it used. It is true you do learn something new every day

Thanks

But when we´re saying how old we are (or someone else) should we use "yaşındayım"? I always thought it works like this:

I am 25 years old => Yirmi beş yaşındayım

Yirmi beş yaşı => Age of 25

Yirmi beş yaşı - n (buffer letter) - da ("in") - y (buffer letter) - ım (I am)  ==> I am in the age of 25

But numbers are adjectives. There is no need for a possessive suffix (and pronominal -n- respectively) in the following word yaş.

It´s more about where the possessive refers, to the person like scalpel says or to the concept of age (like years of age in English).

Yes, this is exactly what I wanted to say - I always thought that it is possesive refering to the concept of age (I meant "age of 25", not "25 ages").

And what might actually add to speakers´ uncertainty is the ambiguity of the question

              Kaç yaşındasın?

because it could be

yaş|ın|da|sın = stem + POSS sg2nd + LOC + ´to be´ sg2nd

OR yaş|ı|n|da|sın = stem + POSS sg3rd + -n- + LOC + ´to be´ sg2nd.

Such a shock for me (a native speaker who has never ever used the form "yaşımdayım") as well!