On Shabbath it is so easy and so close to us to reach out, to extend ourselves a little to HaShem and invite Him into us to spend Shabbath with us, to sit at the Shabbath table of His sons and His daughters.
This is the Neshamah Yetera, the additional Shabbath soul that every Jew receives on Shabbath. The nature of the reception is entirely up to us, when we welcome in this additional soul, and bring it close, recognise how precious it is to us, then we rejoice together in the pleasure of Shabbath.
This relationship is not limited to Shabbath but is open and easiest to us on Shabbath, this is what is meant by the passuk וביום השביעי שבת וינפש - on the seventh day HaShem was [as] nefesh. Nefesh is the lowest of all the spiritual levels of the soul. It is the only level that is clothed entirely within the body, the level that is completely connected to the body. (If I recall correctly even after death the nefesh stays with the body.) On Shabbath HaShem comes down to the lowest levels to truly dwell within us, ושכנתי בתוכם - and I dwell within them.
This is just the smallest bit of a beginning to what the experience of Shabbath is truly meant to be.
One of the best ways to prepare oneself to really be able to make space for and accomodate HaShem as our guest on Shabbath is to accomodate other guests on Shabbath and to recognize within each of them, the Neshama Yetera.
Is it any wonder then, that the first person to actually build such a relationship of closeness with HaShem, Avraham our father, was also known for his unparalleled hospitality? Through hachnasat orchim, inviting guests into our home, we are able to build the spiritual muscles that allow us to bring HaShem into our lives, and what a kindness of HaShem that he gave us Shabbath, the most oppurtune time, to devote our efforts.