When three men or three women have a meal, they should say birkat hamazon, grace after meals together. This togetherness is forged by the experience of sharing a meal, and is sealed by the zimun, the invitation to bentsh collectively. One person says "rabotai nevarech", or in some circles, "rabosai, vir willen bentshen", or possibly even "guys let's bentsh", which is the direct English translation. Then the others present answer, confirming their wish to bless together.
One should not duck out of the zimun, eg by leaving the meal early, except of course in exceptional circumstances. The guiding halachic principle is "b'rov am hadrat Melech," among many people, the King is glorified. Doing a mitzvah together with others is usually better.
The Zohar explains the idea of a zimun, saying "any holy act requires hazmanah beforehand": hazmanah, from the word zman, time, can be translated here as conscious dedication of time. The zimun creates the consciousness in a group that they are about to accomplish something holy together.