Acquisition refers to the first stages of learning when a
response is established. In classical conditioning, it refers to
the period when the stimulus comes to evoke the conditioned
response.
In this stage, some response is being associated with some
stimulus to the point where we can say the organism (person,
animal, etc.) has "acquired" the response. During this stage the
response is strengthened (reinforced) so that it is truly
"learned".
For example, if you are trying to train a rat to press a lever
in response to you ringing a bell (i.e., trying to condition the
rat to press the lever when and only when you ring the bell), then
once the rat presses the lever in only response to the bell, you
can say the response is "acquired". You would then continue to
gradually reinforce the lever pressing in response to the bell to
make sure the response is strengthened.