This expression indicates that it has been only a short period of time since what is represented by V took place.
わたしは、今、家へ帰って来たばかりです。まだ上着もぬいでいません。
I've just come home. I haven't even taken off my jacket.
However, Vたばかり(です) can also be used for something which is not as recent as what is expressed by Vたところ(です). Vたところ indicates the point in time at which the action is completed.
先週、日本に着いたばかりですから、まだ日本の生活にはなれていません。
I just arrived in Japan last week, so I haven't gotten used to life in Japan yet.
今、ひこう場に着いたところです。これからバスに乗って、帰ります。
I just arrived at the airport. Now I'm going to get on the bus and come home.
When modifying the following noun, Vたばかり takes の: VたばかりのN.
生まれたばかりの赤ちゃんはしゃべれません。
A newborn baby cannot talk.
On the other hand, Vたところ cannot be used to modify the following noun.
Vたところ simply indicates the point in time when an action is completed.
Lesson 25-3「弟はねてばかりいます。」
My younger brother does nothing but sleep.
Lesson 25-4「わたしは食事をしたところです。」
I just finished my meal.