What does the word "world" mean in the Buddhist context?

Load Buddha has realize new visions. to communicate those ideas he need new words (for new concepts). Instead of defining new words he sometimes use them with new meaning.(This is one example).

The word "world" has two usages, one for normal meaning as shown in Andrei's answer.

The other meaning is for new understanding about the 'world' we create by our self. It create by 'Six sense doors'.

Instead of using the word "world", '5 Aggregate', '12 Ayathana'(faculty),' 18 Dathu' or 'Dukka'(suffering), 'Bimba'(Illusion), 'Maya', etc also used to as appropriate.

In 'Hemawatha sutta' the dialog goes as.. ....

Hemavata
The grasping—what is it then
by which the world’s afflicted?
When asked about this, please do speak:
how to be free from dukkha?

Buddha
The sensual pleasures five are taught
in the world with mind as six,
having let go of all desire for those,
be thus from dukkha free.

This for the world’s the leading out,
its “as-it-is” declared to you,
and this to you I do declare:
be thus from dukkha free.
...

I believe by "world" Buddha usually means the human civilisation, the society, the world of people:

This world is blind! There are so few who see things as they truly are.

...

Whose Dhamma is well-taught? Who has practiced well in this world? Who in the world is well-gone?"

...

He has made known — having realized it through direct knowledge — this world with its devas, maras, & brahmas, its generations with their contemplatives & brahmans, their rulers & common people.

...

He who in this world takes nothing that is not given to him, be it long or short, small or big, good or bad — him do I call a holy man.

...

This world completely lacks essence \ It trembles in all directions \ I longed to find myself a place \ Unscathed — but I could not see it.

...

He who having been heedless is heedless no more, illuminates this world like the moon freed from clouds.

...

Birth is ended, the holy life fulfilled, the task done. There is nothing further for the sake of this world.

In the quote you have provided, the “world” is the six senses. The Buddha often used the word “world” in a metaphorical sense. Here are some Suttas where "world" is used in a similar way:

SN 35.82:

Then a certain monk went to the Blessed One and, on arrival, having bowed down to him, sat to one side. As he was sitting there, he said to the Blessed One: "'The world, the world' it is said. In what respect does the word 'world' apply? "Insofar as it disintegrates, monk, it is called the 'world.' Now what disintegrates? The eye disintegrates. Forms disintegrate. Consciousness at the eye disintegrates. Contact at the eye disintegrates. And whatever there is that arises in dependence on contact at the eye — experienced as pleasure, pain or neither-pleasure-nor-pain — that too disintegrates.

(repeat for ear, nose, tongue, body and mind-sense)

SN 12.44:

Dwelling at Savatthi. There the Blessed One addressed the monks: "I will teach you the origination of the world & the ending of the world. Listen & pay close attention. I will speak."

"As you say, lord," the monks responded to the Blessed One.

The Blessed One said: "And what is the origination of the world? Dependent on the eye & forms there arises eye-consciousness. The meeting of the three is contact. From contact as a requisite condition comes feeling. From feeling as a requisite condition comes craving. From craving as a requisite condition comes clinging/sustenance. From clinging/sustenance as a requisite condition comes becoming. From becoming as a requisite condition comes birth. From birth as a requisite condition, then aging & death, sorrow, lamentation, pain, distress, & despair come into play. This is the origination of the world.

(repeat for ear, nose, tongue, body and mind-sense)