For example.

Ağaca çıkarken düştüm. 

I am thinking the arken is akin to a while? Like I fell while I was getting out of the tree? 

Another:

Yağmur yağarken dışarıya çıktım. 

It that like while it was raining I went outside. 

I´m thinking that this suffix is like while/during?

you are right. you can find the lesson about this here:

http://www.turkishclass.com/turkish_lesson_362

çok teşekkürler!!!

The suffix is not so much -arken or -erken, but -ken which you can add to almost anything. (-ken comes from iken but I don´t know if iken is used much.)

Çocukken olmak istenen bir meslek nedir? 

When you were a child, what did you want to be?

Boston´da kalıyorken Tom´la tanıştım.

When I was staying in Boston I met Tom.

Apart from this forum more examples here: http://www.turkishlanguage.co.uk/iken.htm 

Yes, it´s er-ken where er=early, soon

er ya da geç = sooner or later

er-ken = when it´s early

It can be translated as above, but it´s percieved as a word because its stem (er) is not widely used in spoken language anymore.

erken = early

In her example "Ağaca çıkarken düştüm" it doesn´t mean early, the suffix is -ken. The -ar is just the suffix for wide tense.

It´s about the suffix -ken, not about "early". But nice to know er means early, I didn´t know that. 

It appers that I saw -erken as erken. Excuse me.