One would use "to take a walk" to emphasize that one is walking for walking's sake, roughly speaking. For example, "I've got some free time, so I'm taking a walk on the beach."
One would use "to walk" in contexts where one is merely describing the physical action of walking. For example, "I'm walking home."
"I'm takingNow, Dictionary.com does give a walksecond sense of "to walk" as "to move about or travel on the beach" suggests the speaker is walking voluntarily and for funfoot for exercise or pleasure" (here). "I'm walking onThis second sense of "to walk" would be the beach"first sense of "to take a walk", onif the other hand,dictionary had an entry for it.
What this means is merelythat "to take a description ofwalk" more strongly suggests that the physical act of walking on a beach, with no other connotationsis being done for exercise or pleasure than "to walk."