1. To approach and to stop someone in order to speak; especially, in an aggressive, insistent, or suggestive way.
2. To approach and to speak to someone boldly or aggressively, as with a demand or request.
3. Etymology: via French and ultimately from Latin accostare, "to adjoin"; from Latin costa, "rib, side" (source of English coast). The essential sense is "to be alongside".

Costa is the Latin word for "rib", and therefore, "side" and accost is formed from Latin ad-, "to" + costa, making the verb accostare, "to bring to the side of, to bring side by side". From this, or from the French derivative accoster, we have made English accost, which first meant "to lie alongside", then "to come alongside", "to approach and to greet"; and finally simply "to greet", "to speak to".