Revelation 11:9

those from the peoples, tribes, tongues, and nations
A fourfold designation indicating global scope—all the peoples of the earth. See Four: the Entire World, the Earth. This is the global community which John was told he “must prophesy again about” (Rev. Rev. 10:11+), over which the beast is granted authority (Rev. Rev. 13:7+), and upon which the harlot sits (Rev. Rev. 17:2+, Rev. 17:15+).

will see their dead bodies
The phrase “from the peoples, tribes, tongues, and nations” generally speaks of a global community which is worldwide in scope and not necessarily restricted within a single city. It is unlikely that we are to understand this as describing a group of people from the global community who are resident in Jerusalem at the time,1 but that the populace of the entire globe is aware of the events which are transpiring. Television or a similar technology would be a natural explanation in our own day. Bullinger, writing before 1913 and the advent of television said: “The older commentators might have felt a difficulty in understanding how the whole earth could rejoice at an event happening in Jerusalem. But in these days of electric inventions, telephones, and wireless telegraphy, we all know how the next day the whole world sympathises or rejoices together.”2

three-and-a-half days
The global audience will not just see the dead bodies at the time they are slain, but will continue to observe the bodies over the three-and-a-half day period. That these are not to be taken as lengthy periods, but literal days, is seen from their lack of advanced decomposition at the time of their resurrection. Their bodies would have probably remained exposed and allowed to slowly decompose over an extended period, but God intervenes and resurrects them on the third day. See commentary on Revelation 11:11. Three days speaks of life and resurrection. See Three: Life, Resurrection, Completeness, the Trinity.

not allow their dead bodies to be put into graves
There are at least two reasons burial is withheld from the witnesses:
  1. Jewish Sensibilities - One reason their bodies will remain unburied is as an intentional insult to Jewish sensibilities which consider lack of burial an indication of being judged or cursed. See commentary on Revelation 11:8.
  2. Trophies to the Beast - Not only will their bodies be withheld from burial, but it seems likely they will be proactively protected from disturbance by scavengers, such as birds and dogs which would normally descend upon unguarded carcasses (2K. 2K. 9:10; Ps. Ps. 79:2; Jer. Jer. 7:33; Rev. Rev. 19:17-18+). They are prevented from burial and protected from scavengers because they serve as trophies which testify to the power of the beast and the victory of the world over the torment which they delivered at the hand of God. So long as they lie inert on the pavement they provide visual confirmation of the superiority of the beast (Rev. Rev. 13:4+).
Graves is μνῆμα [mnēma] which emphasizes the purpose of a tomb as a sign of remembrance.3 Instead of having their own private memorial, they serve as a public memorial to the victory of the beast.

Notes

1 Robert L. Thomas, Revelation 8-22 (Chicago, IL: Moody Press, 1995), Rev. 11:8.

2 E. W. Bullinger, Commentary On Revelation (Grand Rapids, MI: Kregel Publications, 1984, 1935), Rev. 11:9.

3 Frederick William Danker and Walter Bauer, A Greek-English Lexicon of the New Testament and Other Early Christian Literature (Chicago, IL: University of Chicago Press, 2000), 524.

Read Revelation 11