The NMDA receptor is an ion channel and contributes to synaptic plasticity and memory. It is said that calcium ion flux through the receptor is critical for this mechanism. However, there are other ion channels that let calcium ions into the cell, how come they don't contribute to synaptic plasticity (to my knowledge)?
Quibbling about other types of LTP (not mediated by NDMA receptors) aside, this is a good question, with a rather intricate answer.
Basically (NDMAR mediated) LTP is not merely activated by calcium, but rather by CaMKII, which essentially acts a sort longer-term chemical memory for calcium that was once "detected" in a spine. A couple of points quoted from a fairly recent review paper:
[a] bulk calcium signal, when produced by depolarization of voltage-dependent calcium channels, is not sufficient to activate CaMKII.
a calcium signal will stay largely within the activated spine. The next step in the long-term potentiation cascade is the binding of calcium to the four binding sites on calmodulin. Calcium-saturated calmodulin keeps calcium bound for ~1 ms, a long enough time for calmodulin to diffuse within the spine and to bind CaMKII, but too short a period of time to diffuse out of the spine. [...] CaMKII diffuses at a very slow rate (for CaMKII to exit spines may take many minutes), activated CaMKII is mostly localized to the activated spine.
So basically a fast signal (calcium) gets converted into a (spatially) slow but locally persistent CaMKII signal (via calmodulin). As I understand it, anyway.