A hedgerow is kind of terrain feature, consisting of wall-like earthen mound which has profuse vegetation growing on top of it. In CMBN, a hedgerow is an excellent fighting position offering both cover and concealment -- so long as the enemy is on the other side and not very close.
Bocage is a synonym for hedgerow, but it also means the general kind of country where hedgerows are common: farmland divided into small fields with hedgerows in between. This wiki adopts the second meaning for bocage (the overall type of terrain, featuring fields, woodlots and hedgerows), whereas "hedgerow" is used for the particular terrain feature. Note that in the CMBN Game Manual, bocage is used freely for hedgerow.
In CMBN, hedgerows come in two varieties, low and high. (In the Map Editor, they are called Low Bocage and High Bocage.) The two are very similar; the only difference is in how high the foliage on top is. In addition, CMBN also has hedges, which are very dissimilar from hedgerows, although unfortunately they are hard to distinguish visually from low hedgerows.
Hedgerows are impassable to all units. If you order a unit across one and there is no direct path, the TacAI will instead create a path that may be quite unlike what you had in mind. Small gaps in hedgerows allow infantry to traverse them. Infantry may create such gaps using a blast from a demolition charge. Vehicles require larger gaps to pass, which may be created by 2 blasts, or by rhino-equipped tanks.
Hedgerows are great cover. The lower portion is actually a small elevated ridge in the ground, which is impenetrable to fire of any kind. Thus, infantry prone behind a hedgerow cannot be hit by small arms fire, although they can be suppressed. Infantry fighting behind the hedgerow have only their upper bodies exposed, and the vegetation does offer some protection even there. Also, the concealment offered by the hedgerow is excellent, since any prone members of a unit are out of line of sight entirely, and everyone else is behind the vegetation.
This wiki has a Primer on Hedgerows.