An element of the skill of an MC or rapper. Sometimes it is a verb (e.g. "That guy can flow"), sometimes a noun ("The boy's got flows"), often in non-standard English. While to some extent the flow will be dependent on the lyrics, it is more closely related to the execution. Cadence or rhythm may be appropriate synonyms.
Some descriptions of this talent take place as metacommentary within rap/hip-hop songs themselves, usually relying heavily on simile and metaphor to highlight certain elements. For example:

Two pages cause panic, freestyles is frantic
Thoughts is organic, flow is aerodynamic
Mic is volcanic, rhymes spread across the planet
I send out the scribe now the vibes gigantic
Now, I'm internationally known, mental capacities blown
I hope your microphone's accident prone
Raw footage is shown, but only showin scenes of my own
Leavin your periphereal vision in a zone
But not the twilight, from the insight that I write
and recite, in my mic'll be bright, cause I like
the night glowin, it's out of sight when I'm showin
Man I keep it goin, damn I keep it flowin

Rakim's - When I'm Flowin' (from The 18th Letter)

Other artists might differ, but a couple of things stand out from this verse: flow is original ("only showin scenes of my own"), smooth ("aerodynamic"), "organic", but yet overpowering, explosive ("volcanic"). To some extent, it makes new things visible: the mic becomes "brighter" through its exercise.

However, as subjective as it is, the best way to understand flow is by example. Like a good point guard, you can only read so much about his or her work: in order to appreciate the aesthetic you must see them in action. My other favorites would probably be:
Nas - Halftime (from Illmatic)
J-Live - Them That's Not (from The Best Part)
2Pac - Ambitionz as a Ridah (from All Eyez on Me)
Slick Rick - Who Rotten 'Em (from The Art of Storytelling)

These people know how to make and break their own rules within verses and songs. While avoiding both mechanical attachment to the rhythm of the song and any disturbing errors in rhyme or length, they manage to feel like an organic part of the track. One important indicator is that, if you listen closely, you feel that if you knew lyrics, you could rap the lyrics like that and it would still sound pretty good, because they have found a flow that cannot help but match the track. It's infectious, you find yourself saying the lines like they say them. When he or she ends a verse, you feel like the verse needed to end there, not only from the logical structure of the lyrics but the trajectory of accent and emphasis that preceded it. When a rapper flows well, it feels like a well-known drinking song as opposed to a first-time slam poet.

The difficulty of this concept is obvious from the number of tracks with awful flow that even artists esteemed for their flow have. Compare Nas's Illmatic (where, in my opinion, all the tracks are at least good, B+/A-) to It Was Written or I Am.... More than the commercialism, bling, and lyrics, he just doesn't pull it off quite like he does on Illmatic. The lines are disjointed, and he feels disconnected from the track as a whole.

I don't rap, so I couldn't tell you how to do it. I merely present this as a point of departure for criticism of various MCs. Talib Kweli, for instance, sounds like each track he's written is just too short for all the things he trying to say. It's the reason why I can't listen to more then 1 or 2 songs at a time of many otherwise highly esteemed artists. For some reason or another, their ability to "flow" is inconsistent or nonexistent.