What is flowing in the opposite direction to the glomerular filtrate for it to be called "counter-current"?
The filtrate is moving in the opposite direction of the filtrate. It's a loop. Filtrate moves in two directions relative to the nephron, down (from the cortex toward the papilla/through the medulla) and up (from the medulla to the cortex). We'll start with up, because that's where the active transport occurs
Up: as filtrate moves up the ascending limb, $Na^+$, $K^+$ and $Cl^-$ are actively pumped out of the filtrate and into the surrounding ECF. This limb, the ascending limb, is impermeable to water, so water doesn't follow the active transport of solutes and the fluid becomes more concentrated in the ECF than in the tubule lumen. So on the way up, the filtrate becomes more dilute.
Down: the descending limb is permeable to water and to ions along with it, so as filtrate moves down the descending limb, the osmolarity of the filtrate equilibrates with the concentrated ECF. This equilibration between descending limb filtrate and the ECF, makes the filtrate more concentrated, so on the way down, the filtrate becomes more concentrated.
By itself, the active transport of solutes out of the filtrate and into the ECF on the way up the ascending limb, (with dilution again by the water on the way down the descending limb) would seem to make only a small difference, but consider what happens as the filtrate continues to flow, while the ECF doesn't.
Consider this diagram from Constanzo Physiology, Chapter 6:
First, the active transport of solutes out of the ascending limb brings the ascending limb filtrate from 300 mOsm to 200, while the ECF becomes concentrated. The descending limb and ECF equilibrate, and you're left with an ECF and descending limb osmolarity that has gone from 300 mOsm to 400. This gives you the state represented in frame (1). The increase in ECF and descending limb filtrate osmolarity that is caused by active transport of solutes from the ascending limb is called the single effect.
When fluid moves, 300 mOsm filtrate flows in from the glomerulus, replacing the 400 mOsm filtrate at the beginning of the descending limb (which equilibrates with the ECF), but 400 mOsm filtrate from the end of the descending limb flows around the hairpin and continues along the ascending limb, giving you the state represented in frame (2). This new state is the result of the flow of fluid.
Now the single effect operates on this new state. At each point along the ascending limb, active transport of solutes dilutes the filtrate in the ascending limb and concentrates the ECF, which equilibrates with the filtrate in the descending limb, giving you the state represented in frame (3). Here you can start to see an up/down gradient establish. Continue these steps, and you can see how a substantial gradient can form.
After being presented with countercurrent multiplication, students will often ask how it is that solutes and water equilibrate horizontally in this diagram (i.e., between the descending limb and the ECF), but not vertically. This is a different question, and is where you start to need yet another compartment, the blood in the vasa recta. This mechanism is called countercurrent exchange, but is the answer to another question (how come the corticomedullary gradient doesn't dissipate?).
In addition to physiology texts (e.g., Costanzo Chapter 6), you can read one of the most important original papers supporting this mechanism. Originally published in 1959, it was reprinted here in 1997 and available for download. See if you can follow the connection between the data and this mechanism.