There are 39 activities that are forbidden in Shabbat (melakhot , see here). One of them is called in Hebrew hotza-a, i.e., carrying, transporting or transferring an object from one domain to another.
Although this melakha is not explicitly mentioned in the Tora (same as most of the 39 melakhot) there are a few places where this activity is seen as a melakha. For example, when haShem sent the manna (heavenly bread, Ex. 16 ) which the people of Israel would gather everyday as their only source of sustenance, haShem forbade the people to gather, carrying and bringing home the manna on Shabbat. They had to relay on the manna of Friday, which consisted of a double portion.
A second source where carrying objects is called as melakha is found in Exodus 36:6. The people of Israel donated precious metals, fabrics, leathers, stones, etc. At one point, they realized that they had a surplus of materials and Moshe ordered them to stop all melakha (as we know melakha defines the activities done for the building of the mishkan), the pasuq then says "vaikale ha'am mehabi" and the people, following the instructions of Moshe "refrained from bringing" any more things to the mishkan.
This melakha is so important (and its details so intricate) that the Mishna of Shabbat devotes to this subject five of its 24 chapters, and of course most of the tractate 'erubin, ten chapters, are related to this melakha. Maimonides, in his Mishne Tora devotes to hotza-a eight out of 30 chapters and most of the eight chapters of hlkhot 'erubin.
B'H in the following HOTD we will explain some of the details of this melakha.
Le'ilui nishmat haRab haGa-on R' Ya'aqob ben haRab Obadia Yosef, z'l.
Shabbat Shalom!
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Shabbat ends in NYC: 8:13 pm
WATCH here Hilkhot Shabbat from rabbi Ya'qob Yosef z''l (Hebrew).